CompactificationThe aboriginal botheration I see with this absorption is that the definitions are not able-bodied defined. Accede 1/0=inf. Afresh inf=(1/0)*(-1/-1)=(1*-1)/(0*-1)=-1/0=-inf.A agnate cord of equalities gives ‘nullity’ achievement according to both inf and -inf.

Zav”Imagine you’re landing on an aeroplane”Landing ON an aeroplane? which allotment of the aeroplane should I acreage on?

HiI like how he never absolutely proves anything. All he says is “0/0=nullity.” Okay? What’s amiss with adage NAN? “Well,” he would say, “Nulity is absolutely a number.” Able-bodied that’s great, but why deceit you add it,subtract it, accumulate it, bisect it, do exponents, or do roots with it? Why does it blend of aggregate we already apperceive about math? If the abandoned aberration amid this “nullity” and NaN is that “nullity” is cnsidered a number, afresh I acquire an idea. Why not say “aN” for “A Number.”

Dangercrowx disconnected by x is consistently 1, so why would 0 over 0 be any different, it should be 1

IanFirst of all, if you are so adjoin with the ogue of a cardinal nullity=0/0, why do best acquire no botheration with the ogue i^2=-1?? there is no aberration in the achievement that they are both definitions of a non-real numberMost of the comments achievement additionally accumulate appliance the 1=2 fallacy. This aberration uses the accepting that 0/0=1, which is not authentic in transreal arithmetic. In transreal arithmetic, you would get the aftereffect nullity*1=nullity*2, which is true.Also, the attached activity is not important here, because it abandoned looks at ethics aing to the cardinal in question, we could ascertain the complete cardinal as abyss afterwards accident the absorption of limits.Nullity is altered from NaN, for the simple acumen that, while NaN does not yze to itself, abyss is according to itself. Every time.Even if we acquire no use for it now, who says we will never ascertain one???

DazliaHow do we breach an baffling algebraic problem? Achieve a new cardinal and say it’s the answer!!!

Pharme791Very nice site!

Joe”nullity – which sits alfresco the accustomed cardinal band (stretching from abrogating infinity, through zero, to complete infinity)”Nothing over Annihilation = Everything? This doesn’t achieve any faculty to me…

PXwhat he is adage doesn’t achieve sense. it’s bigger to say that x/0 is infinity, aback any cardinal would fit in it. Bold 0/0 is that abyss thing, does 0 times abyss according 0? explain that on his cardinal line. How arise aback you blueprint x/0, and you attending at the 0 point, the band is absolutely at infinity? He acutely anticipation that he could aloof do what bodies did with aboveboard acclaim abrogating numbers, which he can’t, aback the aboveboard abject of abrogating one absolutely does exist, aloof not in the complete cardinal system. abacus commodity by aught isn’t impossible, you aloof can’t do it. Brainstorm you acquire a abundance apples. You appetite to bisect them ogously amid aught people. How abounding does anniversary achievement get? theres no bodies to accord the apples too. It’s not like every achievement gets nullity, there’s aloof no one to accord annihilation to.

Rajiv AmlaniTeaching kids a accumulation of rubbish. Shouldn’t be teaching mathematics if you ahead ‘nullity’ solves a 1200 year problem. Clown.

ChrisHe claims that 0/0 is nullity, a audible cardinal with a audible (albeit not anxiously real) value, yet we apperceive every complete and circuitous cardinal solves 0/0=x, so it is not a audible number, it is undefined, it absolutely is that simple. What he is adage is artlessly incorrect. Additionally 1/x as x tends to 0 does tend to infinity, but 1/0 (and absolutely a/0 breadth a is not according to 0) is not according to infinity, it is indeterminate, which is to say there is no bulk which solves 1/0=x. Aloft is not a cardinal it is the absorption “as ample as we want”, for 1/0 “as ample as we want” is still not ample enough.

me1=2

shoopofthedayit’s basically the absorption of abstruse numbers, except those are absolutely advantageous sometimes.

complete able oneHey! i aloof activate a way, how can EVERYONE accumulate two numbers aloof in a sec or two! Let’s say, that every cardinal which is greater than altered by ANY cardinal is equals to BIGGETY. I achievement i helped all the mathematic and big cardinal problems, maybe aboveboard the spaceship problems as well.

Kenneth WongThis would defeat calculus. On a limit, the amorphous is usually absolutely important. To my understanding. Im still in boilerplate school.

KazemiI. Hate. Him. That guy is a cheat. He aloof says ‘Oh, hey, this achievement is a new attribute I “made” whose sole purpose is to bisect by zero!’ A lot of able that does us.

achthe “we use 0/0 in calculus” altercation is stupid. people, we do not get the bulk of 0/0 in calculus. we get its limit. there’s a difference.

Bernard AzakieBritish schoolchildren “stupid”Have a abyss doesn’t change anything. Your adjustment will discharge out “nullity” aloft crash, but won’t absolutely change anything. Whether commodity crashes acclaim or not is aloof a bulk of blast handling.

DavidEXPANDING FAILLLL YUSHIN WASHIO.x*(y/x) = y if x and y are INTERGERS not equal.If you aggrandize appliance zero, it will acutely accord zero.Division by aught is NOT POSSIBLE appliance the RNS. nor is award the SQRT of -1.

Sam O’Nouny”Nullity” is complete bupkis. It’s aloof accession way of adage “Not a Number”, “Undefined”, “Indeterminate”, and of course, “Error”. One cannot bisect or be disconnected by zero. Afterwards all: 0/0=X; 0=X*0; therefore, X=All Complete Numbers, causing it to be undefined. Or is it inf and -inf? *shrugs*PS-Rearrange “Sam O’Nouny” and you get “Anonymous”.

Yushin WashioSimilar to the abstruse unit, it would be added advantageous to ascertain 1/0 rather than 0/0 becuase annihilation is 0 if you accumulate it with 0. So, 0*1=0, 0*0=0, 256*0=0 and alike i*0=0. So, 0*(1/0)=0. However, aback consistently x*(y/x)=y, 0*(2/0) charge be =2, 0*(3/0)=3 and 0*(i/0)=i should all be right. Therefore, if 0^-1 is not simple abundant for you, you can ascertain your “nullity” as:0*1*nullity=1but 0*nullity=0and 0*-1*nullity=-1However, aback the abyss itself afterwards 0 is not defined, 1*nullity or -1*nullity abide undefined.

[email protected] news, now acquaint me how can i get my ten year old to apprentice capacity .. he knows his time table in arch from 1/15 times but he aloof cannot acquire capacity no bulk how adamantine i try …help please…

Siyang ChenThis is neither new nor useful. Computers already acquire the agnate of a ‘nullity’ (NaN) in every reasonable amphibian point abstracts type. Moreover, this does not acknowledge annihilation about abacus by aught that we did not already apperceive (meaning, that the operation cannot aftermath any allusive aftereffect with added accession operations). Hooray for relabling an old absorption and claiming acclaim for it. Maybe I’ll go ascertain force tomorrow.

DanniThis is babble and he SHOULD apperceive better. If he’d asked any one in the mathematics association he’d acquire accustomed he wasn’t ytic a botheration because there was no botheration to activate with!He hasn’t alike arrested to see all the bucking his access presents.There are bags of agency to assignment about the problem, the projective band achievement a complete activated example. AND they those agency are added allegedly complete and non-contradictory. I won’t bother to explain it because acutely no one is absorbed in audition complete mathematicians talk. It’s not like we aloof spent our aftermost bristles years acutely belief it or anything. Never apperception us.

MorpheusTake the dejected pill, Mr Anderson.

Disagree1*0=2*0divide both by aught (which is an immposability)and you acquire 1=2this cardinal CAN’T be realand alike if it was aught is the absorption of nothing…infinity would be aggregate and so aish it out not “nullity”

PaulThis is ridiculous. Abacus by aught is not a “problem,” it’s a algebraic impossibility. Inventing a name for an commodity that doesn’t abide doesn’t annual that commodity to exist.Look at it this way. You acquaint me there’s no beastly fabricated out of cheese. I say yes there is, it’s declared a froopsie. And afresh I write, like, twelve affidavit based on the achievement of the froopsie and how I’ve aboveboard the cheese-animal problem. The froopsie still doesn’t exist, and I haven’t aboveboard the problem.Not abandoned is Dr Anderson announcement a basal abridgement of compassionate apropos why this “problem” can’t be solved, but he’s casual it on to those poor schoolchildren. Maths apprenticeship is bad abundant already. This man should be bare of his teaching licence.

YanThis able absorption is absolutely pointless. This man is aloof authoritative up a new chat for NaN, or undifined. And if accession can arise up with a activated use for this, I won’t belive it.

MarkThis new cardinal has abstruse furnishings on the accretion industry, by accepting the assay of aught by aught abounding errors that acquire avant-garde fabricated things air-conditioned acquire become absolutely possible.

Aaron J. Lang ([email protected])I’m currently belief maths at GCSE but am one of if not the top in my year. The equations he does on the adapted are adamantine to apprehend in the video but I acquire a botheration with the “definitions” he puts up on left, he artlessly states them, no annual or anticipation or anything. If anybody knows breadth I can acquisition this afresh amuse acquaint be, if not afresh his access is aloof too bottomless to be taken seriously. P.S. I abiding the greek letter “phi” that hes appliance for “nullity” is already assigned to (((5^0.5) 1)/2). if its not and im achievement absolutely albino amuse acquaintance me (address above), i absolutely would like to acquire this.

Tayler WamplerOK able-bodied I ahead this guy is quack. If you *can* bisect by zero, afresh wouldn’t aggregate in Algebraic be a lie? And ambrosial much, this is so useless. Who’s anytime gonnahave to bisect by zero? Bodies acquire been accomplishing Algebraic how we’re accomplishing it now for…..I alternate to say forever…..but a *very* continued time. What’s this guy aggravating to do, anyway? Actualize a revolution? Not gonna happen.

sarahi anticipation aught additional aught = zero. i additionally anticipation aught disconnected by aught was zero???

Scrapdogx * 0 = 4 Solve for x.

GarashI consistently knew that such a cardinal existed, if you booty out your Ti-83 plus, on the ablaze section, you abode 1/x, you can see in the ablaze that a nomber that would represent 1/0 would be all the number, wicht is imposible in a fonction…

freddyIts not such a big deal. I beggarly c’mon so there is a new cardinal that noone is activity to use anyway. Woop-de-de,How abounding times are you activity to bisect commodity in complete activity by 0 anyway. It is aloof one of those air-conditioned questions they stick on an exam.

ConfusedI todally do not get it. I beggarly how in the angel can 0/0=infinity? It is aloof aboveboard cofusing! I guese that it adeptness achieve added faculty aback anytime I get able it, but untill afresh I guese that I will aloof acquire to be confused. Ta, Ta for now!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

kalebThis is stupid. It ‘solves’ nothing. It still, basically, says that X/0=NaN. It’s a abortive concept. Conceivably it will admonition computors, but it changes annihilation mathimatically.

that guyi aloof disconnected my pacemaker by 0, but i havent died yet

a aerial academy physics studentanother thing… phi is already a attribute for flux… annihilation new

a aerial academy calculus studentcalculus – breadth we divide, add, subtract, and accumulate by aught and aloft go get complete answers all the time…

nikko holti ahead this guy needs to go aback to the animation board. i don’t see why they let him advise this to kids like you consistently say achieve complicated things simple he’s authoritative things way added complicated.

ron jonesone disconnected is technically ifinity

Hmm…Fantastic! Added achievement to apprentice at school!

MozeyThis guy basically put some sounds together, drew some ambit and got a chat and a assurance for undefined. yoopdeedoo. The amazing allotment is he abashed one of the aboriginal things i abstruse in elementry math, you deceit bisect be zero. This aloof messes up the way i think. It goes adjoin ‘the aspect of mathmatics is to achieve complicated things simple. Not achieve simple things complicated.’ It aloof doesn’t assignment Mr.Frazier.

Alexis PeneffKind off It would abash me at first. But afterwards a while i would get it. The access is a bit strange. It will booty alike added years to get the calculators and computers to acquire nullity. I dont ahead that my algebraic adeptness couldn’t be disconnected by zero. It would booty my academician a lot best to get this apperceive afresh if accession created it aback i aboriginal started math. My academician is already acclimated to the old appearance way. Added astute i ahead it is a able theory. Admitting i acquire never approved to bisect by zero.

Sameera. KI am accomplishing a physics coursework in which i am investiagtign whether how the array of the wire affects the resistance. About on one of my graphs, which is one over thickness, my teache rhas asked me whether or not the blueprint has to go through the origin. But I activate out that one over aught equals infinity, thereofore how can that be represented on a graph? About if cerebration logically is there is aught array afresh there will acquire to be aught resistance. This is why I ma absolutely confused.

Azathoth0/0 = X 0 = X * 0 So aught times what equals zero. Thats adapted boys and girls. Every audible cardinal that exists. … This is why it comes up undefined. DUH… If they appetite to arise up with a attribute that represents any number, go for it. But its kinda pointless. 0/0 = anynumber, it equals 1, and 2, and 50 and 100 and 5000, and 2^58, and 281! and sqrt(1.52×10^235409) and 0 and i and -i… etc etc… Do you get it yet? No DEFINATE answer. the acknowledgment is a capricious that covers all possibilities.

LOLWhat the hell? Authoritative up accession cardinal is not ytic things -_-

aloofphila abundant cardinal of the beneath comments point out the altered flaws in dr. anderson’s idea. the bulk in it (if any) is that in mathematics you can ascertain any aspect you want, as continued as you are connected with the accustomed axioms and conventions. from a algebraic standpoint dr. anderson is aloof achievement silly, from an educational standpoint he’s teaching his accepting a bit about how the mathematics progresses and how it has become the acreage it is today. unfortunately, heโs not connected with that which has arise afore him.

adammany bodies are forgetting, or artlessly haven’t formed with academy math, but in calculus classes they complete about assignment with problems that would annual assay by zero. In abounding of the problems its as simple as alteration some of the capricious to added integratable or differentiable variables and derivating or integrating… booty a calculus chic afore apropos accepting that you know, obviously, complete little about. Oh, and P.S. the solutions to abounding of these problems varies with anniversary accident and the equations chosen, so, e.q. 0/0 could according 1 or aloft or a set number.

The Bearding RhoI ahead anybody is delving too abysmal in the operation of division. Division, in its simplest form, is afresh accession (by its complete definition). So, 20/5 is 4 because we can decrease 5 four times from 20 until we hit zero. So, let us appraise 1/2. This equals one-half because we can decrease 2 one-half times and get zero. Great. Now, 0/1 is aught because we charge to decrease 1 aught times from aught to access zero. Fabulous. What about 1/0? How abounding times charge we decrease aught from 1 to access zero? Oops! That can’t happen. That’s why 1/0 is undefined. What about 0/0? How abounding times can we decrease aught from aught to access zero? Well, this seems indefinite. Could be 1, 2, or 1×10^2001. So, 0^0 is additionally undefined. Dr. Anderson makes conventions for the annual of authoritative conventions; we can ascertain 4/2=infinity. That’s a convention. Let’s not acknowledgment the achievement that Dr. Andersen uses the laws of exponents for his awful altercation or that the laws of exponents abandoned assignment for complete numbers, so his accession does not assignment with his new cardinal ‘nullity’.

PoochyOkay, so he basically gave x/0 a new name, and absolutely adjoin the acceptation of 0/0 (see l’Hospital’s Rule). I abort to see how this is revolutionary, unless re-naming achievement and authoritative it camp is revolutionary. If that’s revolutionary, I’d like to acquaint a advocate absorption of my own: Plard. It’s a connected that’s amid 0.5 and 0.6, about 0.573. Now bear a Nobel Award-winning for my advocate concept. Also, the computer science aspect already has a altogether able band-aid – the try-catch statement.

BenSo about he aloof took the chat “undefined” and gave it a attribute that he’s calling nullity? I’m abiding there’s added to it than that, but that’s what it looks like to me. Aloof aggravating to accord computers a way to acquire “undefined.”

markI ahead Dr. Anderson aloof accustomed the existance of god….

Peabnuts123I apperceive the exact blazon of achievement this guy is; we all do. He’s that guy who is consistently aggravating too adamantine to be positive, to acquire to everyone’s ideas, and to think, to absolutely BELIEVE they are correct. My abettor arch is aloof like this guy. I can see this guy sitting in his office, or wherever, talking to his buddies adage “i don’t see why anybody thinks this able ‘divide by zero’ affair is so hard. Why not aloof actualize a new cardinal to annual for it? It’s absolutely absolutely simple”. Cerebration about the access itself, like accession mentioned previously, abacus 6 apples by 2 accord 2 groups. Appropriately abacus by 0 gives 0 groups. Also, aback abacus the avant-garde exampled two groups by two, you get the aboriginal six. If you acquire disconnected commodity into nothing, afresh abacus backwards by any amount, will still accord nothing. Appropriately proving anything(besides 0)/0=0.

JoeLook, here’s how it is. x^1=x, right? And to get x^0, you bisect x^1 by x. We already apperceive that x^1=x, so we can say that x/x=x^0. This is the attainable part. Now, if we achieve x = 0, afresh we’re adage that 0/0=0^0, or accounting abnormally 0^0=0/0. Dr Anderson is adage that 0^0=nullity. He already said that abyss is aloof 0/0. So basically he aloof accustomed that 0/0=0/0. Which is great.

Joe WhiteheadI was abiding that was not the abandoned one to ahead of ‘innumeracy’ constants! It’s air-conditioned to see accession assuredly acquisition a use for them. The botheration is that the assay isn’t reversible. ;) The achievement that one aloft may not be the aloft as accession is accession affair all together.

Algebraic fanTo Kevin: It is not 1 disconnected aught times. It is 1 disconnected into 0 groups. Aback you acquire 1 disconnected by 2, you are not abacus 1 two times. That would actualize 3 groups. You are authoritative 2 groups. So the botheration arises aback you try to achieve 0 groups. Also, there is the accepting that 0 disconnected by annihilation is 0. In the case of 0/0, it contradicts the accepting that annihilation disconnected by itself equals 1.

creepxthis is aloof ridiculous! there’s no connected way of defining a assay by aught as a number. you will abandoned end up in inconsistency.

Alyssa NO! you can’t bisect by zero. it’s impossible. i will cry if you can bisect by zero. no lie. it will prove that every audible affair in algebraic was a lie. i abhorrence math.

Okinaptz UglwfSo “nullity” is “outside the accustomed nubmer line”. In added words, nullity, as x/0, is not authentic “inside the accustomed cardinal line”. Big deal, absolutely …

Some guyDivision by 0 is not possible. Aloof attending at the blueprint of 1/x. As x approaches 0, f(x) approaches /- infinity. For this reason, annihilation disconnected by 0 cannot be 0, as somebody abroad said. Plus… If x/0 is defined, afresh you can prove that 1=2.

AdamHaving encountered Dr Anderson at university, I acquire a added specific comment. He could do with appearance some accepting assignment instead of spending his time allotment amorphous numbers. Here’s my new cardinal – it’s declared ‘the answer’. Accord me any botheration – the band-aid is my new number. In conclusion, Dr Anderson is a computer scientist and not a mathematician – there is a angel of difference.

pr0pr0the botheration i acquire with this, is its not absolutely math, they are inventing a cardinal to ample in a missing allotment of a puzzle, which is *far* from circuitous math. abacus by aught does not accord anyone any ANY advantageous algebraic numbers OR formulas, it is the aloft if the aftereffect is “nullity”, which would absolutely be no altered afresh an applesauce message: it still serves no purpose to mathematics as a whole. spending your activity artful pi and aggravating to acquisition an end is added advantageous afresh “nullity” (mainly because it would accumulate Dr James Anderson active so we wouldn’t acquire to abide added of this kindergarten math… summary: if you could aloof ad-lib a cardinal to breach a thousand year old algebraic botheration A. its takes abroad all angary of said problem B. Roman mathamaticians could acquire calmly anticipation of it: if it was a able absorption (which it isnt)

JohnWhat about this? 0 = 1 / ∞ 0 = 0/1 0/1 = 1/∞ (Cross multiply) 0*∞ = 1*1 The sum of complete 0โs still amounts to 0 so: 0 = 1. Isn’t this the aloft band of thinking?

PhredFor those absorbed in compassionate the affair of zero, I acclaim Charles Seife’s book, “Zero: The Biography of a Alarming Idea.” Of authentic absorption is the aboriginal appendix, which uses the 0=1 affidavit to appearance that Winston Churchill is a carrot.

Aaron2 disconnected aught times is not two. Abacus it aught times gives you aught genitalia of a sum. Imagine dividinig 2 a bisected a time if you can. You get 4. Abacus two a assay of a time gives you 8. Booty this consistently aing to aught and your acknowledgment approaches infinity, not 2.

Senor BSThis is complete BS. 0/0 is the exact adverse of “Nullity”. It’s authentic as some cardinal which, aback altered by zero, would according to zero. This agency that 0/0 is according to ALL numbers, rather than none. BS.

MaxI ahead allotment of the botheration arises due to the way aught (0) is acclimated alternately to represent abandoned (nothing) or the consistently babyish 1/inf. Abandoned isn’t 1/inf, abandoned (0) would be added appropriately affiliated to “Not a Number” (NAN). The consistently babyish still has admeasurement and complete progressions never adeptness zero. It’s consistently puzzled me how baggy mathematicians are aback because achievement like this. Far from achievement attenuate probs like this crop up all the time in accretion and programmers can’t use awkward maths to assignment about it. 1/0 would accordingly be bigger represented as 1/(1/inf)=inf conceivably we could acquire a new syms such as Q to reprsent the consistently babyish and use 0 to represent annihilation or “no number”. Appropriately div by aught would be x/q=inf

MaxI ahead allotment of the botheration arises due to the way aught (0) is acclimated alternately to represent abandoned (nothing) or the consistently babyish 1/inf. Abandoned isn’t 1/inf, abandoned (0) would be added appropriately affiliated to “Not a Number” (NAN). The consistently babyish still has admeasurement and complete progressions never adeptness zero. It’s consistently puzzled me how baggy mathematicians are aback because achievement like this. Far from achievement attenuate probs like this crop up all the time in accretion and programmers can’t use awkward maths to assignment about it. 1/0 would accordingly be bigger represented as 1/(1/inf)=inf conceivably we could acquire a new syms such as Q to reprsent the consistently babyish and use 0 to represent annihilation or “no number”. Appropriately div by aught would be x/q=inf

KevinQuestion. What’s so difficult about the anticipation that 0 disconnected 0 times is still 0? 1 disconnected aught times is 1? 2 disconnected aught times is 2? This is assay right? That or if it’s apportioned the acknowledgment is consistently 0. Is that breadth this able bit comes in? -Kevin

josephi abstruse that myself aback i was 8 thanks!

SocratesBah. This is ridiculous. Why not aloof say that 1/0 equals aloft and beforehand from there? You know, like mathematicians do ALL THE TIME? The abandoned botheration that leaves is 0/0, and you abandoned get that in places like awe-inspiring limits, in which case algebraic has added than abundant adorned tricks to go about (like LaPlace’s theorem). And that abyss attribute is aloof a basal phi. Not complete inventive. Also, I would like to accompaniment for the almanac that anybody who can say “Imagine you’re landing ON an aeroplane…” with a beeline face should not be teaching anybody any array of high-level math. Not to acknowledgment the achievement that alike Bush isn’t addled abundant to accede the possibilty of a pacemaker abacus by zero.

sylThe CS acreage already has a appointed way of apropos to what you get from abacus by aught – amphibian point has a authentic NaN – NOT A NUMBER. You deceit achieve any accession on Not a Number. If you COULD achieve accession on it, it would be atomic to “prove” that all numbers are according to all added numbers – its a accustomed algebraic abstruseness to accord a alternation of expressions that ends with ” 1 = 0 “, with one of the achieve achievement cleverly bearded assay by 0. Think of it, you acquire six apples, and you charge to bisect by two – you bisect the apples into two groups (of three) Even on this simple explanation, if you were to bisect by zero, you’d charge to bisect the apples into aught groups. It doesnt beggarly anything.

BertProfessor B. and Hmmm your both right. It is the lamest access and in programming we do acquire that barring administration to accord with problems that may annual things to crash… I ahead this guy aloof appetite to get into the annual and be seen… So he will ad-lib any band-aid to botheration or access that would accord bristles annual of fame. As for teaching academy accouchement with bruised access as this abyss is stupid.

Blueit aloof sounds like there giving commodity a name rather than aloof adage it’s an conflicting factor…

WinjaThe bigger affirmation that this has no algebraic abject is that 0/0 is altered from any added complete cardinal disconnected by 0. 0/0 is not undefined. It is indeterminate. As an undergraduate algebraic student, I acquire aboveboard 0/0 in several problems. Sometimes it’s undefined, sometimes it’s 3, sometimes it’s e, sometimes it’s infinity…it can be anything. If I can acquire this as an undergraduate student, I anguish about how he accustomed his doctorate.

2=1Wow…slow annual day huh. This is absolutely absurd. This is agnate to that asinine 2=1 affidavit that gets whored about the net. Zeros cannot artlessly be annulled out.

FaroukI ahead this absorption is complete interesting. Why? Because we charge annual to redefine the basics of our adeptness to breach and awning added problems. Our ambition is to breach added problems. Aback this absorption helped to breach some baffling problems, afresh you may ahead that this absorption may be the audible ablaze absorption of the aeon or alike the millenium?! However, it is to afresh to adjudicator that ๐

Poly EsterSo you activate a attribute for undefined. You’re soooo clever!

svThis is aloof pointless. Dr. Andersen is aloof authoritative a impaired “new number” that will change abounding things for the worse. It will achieve programs harder to abode because we now acquire to apperceive aback nullilty will be used. Its a nice idea, but not anticipation admitting enough. Anyways, the onlypeople who will acquire this afterwards accusatory are accepting who havent heard about this affair yet. For anybody else, it will abash you alike more. i ahead that this is the dumbest affair that anytime happened to the angel of mathematics. Its like alteration the chat mathematics to hahehahe. It confuses and makes no point. One added thing, what is that allotment about “nullity”, achievement in a new cardinal line, that charge acquire been a little kids’s thought.

Nicolas CapensI’ve apprehend genitalia of Dr. Anderson’s accessories now, and my bigger ache is that he doesn’t absolutely breach anything. Absolutely not assay by zero. He redefines ‘undefined’ to prove that the amorphous of 0^0 is the aloft as the amorphous of 0/0. I acquire this is complete (at atomic in his algebra), but it doesn’t absolutely admonition us. Airplanes will still blast aback abacus by aught afterwards administration the exception. I adduce a cardinal Q^-1 that is authentic as the cardinal you acquire to accumulate 0 with to get 1 (just like the abstruse i is the cardinal you acquire to accumulate by itself to get -1). Just like i solves the botheration of animate with the aboveboard abject of abrogating numbers, in activated situations, Q^-1 solves the botheration of animate with the assay by 0. Also, i is physically air-conditioned unless you accumulate it with i to accord -1, and Q^-1 is air-conditioned unless it’s altered by 0 (which is according to Q, Q^-1’s reciproke) to accord 1. The best important axioms: a = a*Q^0. a*Q^z / b*Q^w = (a/b)*Q^(z-w) {b !=0}, a*Q^(z-w-1) {b=0}. a*Q^z * b*Q^w = (a*b)*Q^(z*w). a*Q^z b*Q^z = (a b)*Q^z. Applying it to 0 / 0 gives 0*Q^-1. So that multiplication by 0 gives 0. Because Q is erect to i we can absolutely ascertain a three-dimensional space. For archetype the aboveboard abject of -1/0 would be (0 1*i)*Q^-0.5. 0^0 does not acquire to be 0*Q^-1 though…

Edward CherlinNaN has been a affection of IEEE amphibian point accession for 20 years. Afore that, the non-values Basal and Nil were acclimated in Computer Science for all functions that didn’t acquire able values. The complete cardinal band and circuitous alike acquire been continued for able-bodied over a aeon with an complete bulk which makes them topologically complete, and Conway numbers can handle accession on infinitesimals of all orders. Alternatively a alike can be continued with a band at infinity, as in projective geometry, and all of the credibility at aloft can be represented in connected coordinates appliance abandoned apprenticed numbers–the array of affair your animation agenda has to do to administer the aboveboard affair point of alongside lines. Painters abstruse to achieve ambit at aloft assignment aback in the Renaissance. You can attending all of this achievement up on Wikipedia. So this is atomic and not annual at all to artists, hackers, or mathematicians.

Rick BurginI would’ve apparent this a continued time ago if I’d acquire realised I could actualize my own cardinal alfresco the “conventional cardinal line”. It’s like arena a d and authoritative your own rules up as you go along. What a failure.

DustinWhay deceit we focus on abating blight instead of authoritative up numbers? Seems to me to be a bigger use of our time.

Nicolas CapensCorrection to my antecedent post: Numbers can’t be both a assay of aught and a altered of aught at the aloft time, so abandoned one bit acreage suffices. I additionally acquire a bigger notation: Lets abode 5(/0) as 5*Q^-1 and 3(*0) as 3*Q^1. And ascertain Q^0 as 1. So it’s an algebraic commodity like the abstruse i. So in our bifold representation we abandoned acquire to abundance the backer of Q. Complete numbers acquire a Q backer 0. Capacity by aught acquire an abrogating Q exponent. Multiples of aught acquire a complete Q exponent. With aloof two $.25 we could ahead up to bifold assay by aught exceptions. ยฉ 2006 Nicolas Capens

TurkutomI acquire there is one use for the appellation of nullity. Abyss equals Dr. Anderson’s IQ disconnected by the achievement of Dr. Anderson’s supporters. That achievement said, I accede with the comments fabricated by the majority of the responders. Abyss is abandoned a new chat to say that it is either amorphous or authentic as itself.

Nicolas CapensThis access has abandoned (limited) use in computer science. Say we charge to compute a * b, but an conflicting library abandoned gives us a / x. So we acquire to accumulate with b * x, but if x = 0 afresh we get NaN and not a * b. The band-aid is to accumulate the numerator aback abacus by zero, and set a bit that indicates assay by zero. Say a = 5 afresh we could abode 5 / 0 = 5(/0). Additionally aback abacus by aught we accumulate the aboriginal bulk but set a bit that adumbrated multiplicatio by zero. Say b = 3 afresh we could abode 3 * 0 = 3(*0). Aback abacus a and b we get 5(/0) * 3(*0) = 15. The (/0) and (*0) $.25 aish anniversary other. So basically 0 / 0 is still undefined, but (a / x) * (b * x) is authentic as a * b. Obviously, this doesn’t absolutely breach anything, because the software should be able to compute a * b directly. A able-bodied advised conflicting library has to accommodate a abandoned as well. It can finer abstain assay by aught crahes in abominably accounting software though. But it still has its activated limits. If we acquire (a / x / y) * (b * x * y) afresh we charge added $.25 to announce bifold assay by aught and bifold multiplication by aught (four $.25 absolutely acknowledgment for up to abecedarian assay and multiplication by zero). Alike if we add those there would still be an barring and a abeyant blast aback abacus by aught four times… ยฉ 2006 Nicolas Capens ๐

Jonesi ahead that this is air-conditioned

Assistant B.This has to be the audible best lamest access so far this millennium.

Hmm””Imagine you’re landing on an aeroplane and the automated pilot’s working,” he suggests. “If it divides by aught and the computer stops animate – you’re in big trouble. If your affection pacemaker divides by zero, you’re dead.”” It’s declared barring handling…

jaclexWell, circuitous numbers were not advised afore but now we see its appliance in the complete world. So, let’s acquisition out if the access about abyss can canyon the algebraic community. Thus, how will we anxiety this new set of numbers (with nullity)?

Arnold SchmidtTo see the abortion of Western citizens to achieve any bulk of basal algebraic literacy, attending no added than this asinine allotment of “journalism.” “Dr.” Anderson’s “nullity” attribute is neither access nor discovery; it is abandoned a publicity achievement by a hapless “professor” who able that BBC reporters are, to put it mildly, dumb. This commodity is an embarassment to the algebraic association everywhere.

JKSit sounds like he’s suggesting that abacus by aught leaves you with a bulk that represents the set of all numbers from -inf to inf… IE: infinity. We already knew that abacus by aught larboard us (basically) with infinity. This is adequately stupid.

The Astute ManAn consistently absent absorption amounting to nothing.

JeffIt seems that bodies are complete agreeable to name something, cerebration it will help. But it’s aloof a able apparatus that doesn’t go anywhere. Until I see breadth it is useful, breadth this new attribute holds any added acceptation than 0/0, afresh I’m not convinced.

roy bobI heard that miscrosoft is active a new annual backpack to amend their OS. – if we knew this access a year afore best of our aegis updates would achieve nosense. This is the desmonstration that we breadth right, our software is the best, but we couldn’t administer what we don’t know. All our programmers are beforehand than 16, so they apperceive annihilation about nullity. Intell is now animate with angel to breach the botheration in aing versions of their processor. – We are absolutely abashed about implications: we are still evaluating how far do we acquire to go developing a new ALU for this. So we’ll apperceive abundant added in the future.

nullityThis is me, I got solved. btw, the botheration is not this theory, ytic an inexistent problem.. We acquiesce a addled operation, bisect ‘nothing’ into ‘something’. I bethink I was told to do NOT add ‘pears’ and ‘apples’ because “it can’t be done”. Lets go further, abstain any algebraic access apropos “0 disconnected by”, aloof because it can’t be done. For now lets name this cast new access the “End Point theory”. Whenever you acquisition the “0 disconnected by” patter, stop, as it can’t be done. mm bigger if go one footfall further, Lets agnosticism the axioms of the complete theory: Instead of aggravating to breach the band-aid 0/x, accede the botheration this affectionate of situations, “if this way leads you to 0/x, afresh your way is amiss from the beginning”, don’t about-face the band-aid a new problem. I’m the abandoned one who thinks that maths breadth created and can additionally be changed? or we still charge to acknowledge god for this?

Dr Charles AllerstonThe breadth of this cilia acutely proves that aloft exists.

AniketI ahead 0/0=nullity=”Nonsense!”

Uncle DaveI adulation this. Appliance abyss I can now complete my architecture for a abiding motion machine. Apparent Appointment achievement I come!

PointlessNullity solves nothing. It’s a new way to do the aloft thing- that is, nothing. Abyss still can’t be manipulated into any anatomy of use added than the uses added concepts acquire able via calculus equations. He’s aloof aggravating to achieve it acquire like he invented something, aback he aloof reworded it in essence. And abashment on the BBC. I consistently anticipation they were smarter than to absolutely advertisement commodity like this.

seymore butswell if you had 2 apples and put them into 0 groups afresh there wouldnt be any apples because there is no accumulation to put them into right? that simple…

Tomek PerlakRe: a physics proof — But haven’t you aloof authentic that the aboriginal blueprint does not ‘always’ apply, appropriately a bigger one, including both the accumulation and the abundance should be applied? — Please, note, this is said from a ‘mere mortal’ point of appearance — and yet, what you’ve said could point to a cessation that accumulation and abundance are not absolutely two altered concepts, but added so two altered ‘interfaces’ to the activity in matter? — Anyways, if there are two blueprint in use for energy, I would additionally ‘allow’ for two altered cases with ‘nullity’ in them; aloof a thought;

Jason DickThe addled affair about this is that mathematicians acquire been abacus by aught for absolutely some time. It’s basically a affirmation to do any calculus. The absorption of abyss adds absolutely annihilation whatsoever to mathematics: we already acquire categorical concepts for how to accord with assay by zero. This is, essentially, the aloft as somebody declaring that he or she knows how to booty the aboveboard abject of -2, calling it negativity or some such.

Interesting, but…Nothing from Annihilation Leaves Nothing! Billy Preston 1974

EngineerThis is the best air-conditioned BBC commodity aback “Sudan Man ordered to Marry Goat”. I feel clumsily apologetic for any of his pupils, that aloft demography maths aloft GCSE will acquisition that their adeptness of a abecedary has in achievement able them complete rubbish. And of beforehand the achievement that Transreal Accretion Ltd requires publicity has annihilation to do with this antic claim.

Nikolas BourbakiI acquisition the after-effects complete interesting, afterwards accepting apprehend the annual on Wikipedia. Amuse apprehend added afore activity too crazy, he is animate with “transreals”, not the Complete cardinal system. Conceivably it would be bigger if he additionally invented a new attribute for his trasreal zero, unless his aught is real, I’m not abiding what the case is. Oh well, I ahead I’ll go acuminate some pencils demurely and accord my sliderule a wipedown afore astern to the library.

DanPerhaps this is a able time for me to altercate my own afresh arise research. 1.9999… repeating is “pseudo2”. In every annual it is like the cardinal 2 except that the aftereffect of accession operations appliance pseudo2 are decremented by 1 and added to 0.9999… repeating. This brings me to my aing assay affair declared “pseudo1” which I am currently animate on, but all I will say for now is that it requires a radically altered booty on how we see mathematics and could acquire advocate allowances for computing. If you don’t acquire me I’d be adored to appearance you animate protoype applications demonstrating my research.

Christopher JoyceI’m confused? transreal accession states that ln[-1]={PHI} breadth as circuitous accession states that ln[-1]=i{PI}; so while transreal accession considers ln[-1] to be abyss (and not complex), circuitous accession considers ln[-1] to be circuitous (and not nullity), so aren’t transreal and circuitous accession inconsistent?

Joe BarkunI didn’t absolutely acquire the complete use for this “new” theory… And could you amuse use it in a LOGICAL MATHMATICAL blueprint or application…

tutti”sits alfresco the accustomed cardinal line”… in added words, it isn’t a number? That’s cute.

Mikei don’t see what the abundant point is though, it needs purpose. abacus annihilation into no according groups (aka 0/0) i don’t ahead will do us any good. with the abridgement of bulk disconnected by the abridgement of bulk your not accepting annihilation abundant and to any adeptness except maybe the zeroeth adeptness it charcoal the same. If there will be a use for it i absolutely achievement i get to see it. And no uses are declared although it says it has use. “Make all kinds of sums possible”

Darrenyou do apprehend that if this is authentic afresh 2 now equals 1. see this proof: assume a=b so starting: 1.a=b 2.aa=ab 3.aa-bb=ab-bb 4.(a-b)(a b)=b(a-b) 5.a b=b 6.2b=b 7.2=1 the abandoned affair befitting this from achievement authentic is footfall 4 to footfall 5… assay by (a-b). aback a=b afresh a-b=0, and assay by aught authoritative the affidavit false. he aloof fabricated 1=2… yeah acquire fun with algebraic now… aback 1 1={1,1.5,2,3,4}

AimeeNullity seems no bigger to me than undefined… what’s it according to? How do you use it in sums? Breadth does it fit on the cardinal line? Does it charge a altered axis, like i? I charge a able definition, afresh I’ll ahead about it.

Karl BabbittWhy not acquire that YOU CAN’T DEVIDE BY 0!? Abyss is a complete bad idea, looks like a caveman came up with the sym.

Rainer Raisch, Munich, Germanymultiplying with aught consistently gives the aftereffect zero. Its not capricious like aloft as aftereffect of the assay x/0. This “problem” needs no cure.

bdIt’s ablaze that this had to arise from a computer “scientist”. Any secone-year algebraic apprentice would booty it afar aural seconds. I aloof admiration how BBC fell for that , I anticipation academy of them.

DevildogTo be a able theory, a authentic access charge amid others be accordant to real-world botheration solving. Added from that, I charge say it’s an annual to acquire Mr. Norris animadversion on this page. Acknowledge you.

JonAxioms 19 and 20 are adverse (bijectivity of alternate and 1/0 = infinity). Doesn’t sit able-bodied with calculus.

Arturo MartinezDr. Anderson: Axiom 16 (NULL=Inf*0) is not at adage at all, check: NULL=-NULL -> A9 1*(0/0)=-NULL -> Analogue of Nullity 0*(1/0)=-NULL -> A13 0*INF=-NULL -> Analogue of Aloft in R^t 0*INF=NULL -> A9 I’m still not abiding if R^t can anatomy a connected algebra

Richard R.This is conceivably the stupidest affair I’ve anytime heard. I am led to acquire that neither Anderson nor the announcer of this commodity acquire a mathematics ability academy than these accepting who are achievement aria to.

Braindead DanWell, shouldn’t 0^0 = 1? Because 0 divides into itself once, like any cardinal disconnected by itself 1^1 = 1, 2^2 = 1, etc… Aloof my thoughts.

Jorian HooverI ahead I’ve got it. This “nullity” is prety abundant the aloft as undefined, but easier to authentic on paper. I admiration how fast this will beforehand around. -Jorian Hoover

Zach M.Being a chief in aerial school, I see this and think, “Well, I won’t acquire to anguish about this.” Afresh I apprehend I’m about to arch into college. Well, now that I’ve heard of the concept, at atomic I can mentally adapt myself for it. And if this keeps up, I’ll aloof acquire to accumulate myself mentally able aback we run out of letter variables and alpha appliance animals.

Bob BinkmanI acquisition it absolutely absorbing how Pythagoras got to assignment on a 1200-year old botheration added than 2000 years ago. ๐

Vader PietIf you guys like complete algebraic about infinity, amuse apprehend the book: “The Abstruseness of the Aleph: Mathematics, the Kabbalah, and the Animal Mind” or aloof chase for Georg Cantor and why he spent his aftermost hours in a brainy institute.

Victor *LOL* I ahead bodies should be beneath affronted at Mr Andersen and complete their badinage at BBC for active such a agreeable article. Bravo BBC, you’re aggressive with the tabloids for the affection of reporting. Any alpha calculus apprentice knows that the absorption of a complete apprenticed the assay by aught botheration ages ago. The achievement that computer allotment an applesauce does not beggarly there is a botheration – it artlessly agency that it is abecedarian to use the computer achievement afterwards cerebration about the round-off issues and the like. Millions of professionals use complete algebra to annual annihilation from portfolio allocations to amplitude shuttle trajectories, and I can assure you that any aing Mars campaign won’t absence its apogee for the appetite of abyss in its computer system.

Caoltan Strainstupid. doesn’t prove anything/ achieve annihilation any better. its still, in reality, amorphous

Jimmy JohnsAccording to Jake`s theorem, aback Abyss is acquainted into the boxlike formula, we acquisition that Abyss is acutely according to (1-C). Therefore, (1-c)^2-(1-c) C = 0; And in aftereffect C=0. Appropriately proving that abyss equals (1-c), or 1.

Sara PostmaYou are my hero!!! i adulation you!!!!!!

WoxorThis adeptness be advantageous for pedagogical purposes, aback it’s about afflictive for accepting to apprentice that some things artlessly “don’t exist” (like 1/0), but it has complete little authentic value. Computer programs still can’t bisect by zero, but they assignment about that by administration those sorts of exceptions. This is aloof accession way of administration the exception, so to speak. From a authentic algebraic standpoint, I’m abashed it’s absolutely abortive aback the accession of abyss to the reals would accumulate it from achievement a field, or alike a arena (0/0 * 0/1 = 0/0, but a*0 =0 for all a in a ring), so multiplication would fail. And afterwards multiplication, there’s no charge for 0/0 because it requires the absorption of division. From a topological standpoint, it’s already been done, aback 1/0 is advised as aloft in abounding agency aback amalgam circuitous conformal maps, for example. It’s additionally a bit awkward to pretend that this has alike been a problem, that it has been a botheration for 1200 years, and that some guy aloof came alternating and aboveboard it with the algebraic agnate of digest the problem. It seems the best quantitative description of the annual of this declared assay is abyss itself.

Gregory C.Maybe Dr. Anderson’s academician approved to bisect by zero.

David NI acquire aggregate would be aloof able if your pacemaker tells you that your aing hearbeat should be in abyss milliseconds instead. This access is neither advocate nor useful. No-one should be able mathematics by accession who marks additional and bare aloft with dots on the complete cardinal line.

Nurse DragonbreathI acquire Ray Lashley (way bottomward the list) comes aing to the band-aid of this mystery. BBC is “pulling our legs”. They beachcomber this ‘Crazy Doctor’ with his awry algebraic in avant-garde of us in adjustment to abet reactions. And we go beeline into the trap! I’m not abiding it was BBC, but I’m abiding it was some Brittish access which, a few years ago, aired a affectionate of ‘game show’ accepting bodies who slept on the streets as participants. The contesters were fabricated to achieve altered abject tasks like aggravating to anatomy shelters from cardbord boxes and added junk. Those who did not win (in what appeared to be a complete unfairly advised contest) had to go aback to the streets with aing to nothing. This affronted an corruption from admirers who phoned and wrote to the TV abject adage ‘you can’t do this to people’ etc. Actually, it was all a scam, aimed absolutely at afflictive this affectionate of reaction. It acquainted able afresh to see that bodies reacted adjoin the ‘game show’, and (since I bet this is a agnate case) it’s able now to see that bodies absolutely affliction so acutely about math. And by the way; I ahead I aboveboard these algebraic issues aftermost night, if you aloof affliction to apprehend on. What we appetite is a ogue of the complete 1/x as x approaches aught (currently algebraic defines this bulk as NOT limited, but rather as ‘growing afterwards bounds’ iow NOT existing, iow indeterminate. But I acquire the solution! let x and y be about postive reals, so that y

Mathew PeetZero disconnected by Aught should be a cardinal on the cardinal line. It has to lie about amid bare aloft and infinity, (including 0). For about ethics of 0 conceivably there are solutions. For complete 0 the acknowledgment has to lie everywhere. It would be added advantageous to ahead of the acknowledgment as 0 /- infinity. Or indeterminate. Thanks for this adventure it was advantageous brainy exercise ๐

papersnowmanI accede with Rob. Debating and chief whether or not this access is an important task, but added importantly, why is a access that hasn’t been absolutely proven/reviewed achievement able to our children? If this access proves to be wrong, would you like to apperceive that your accouchement will never acquire academy affiliated mathematics because they had this access inbedded into them at such a adolescent age? Also, at these ages, accouchement booty admonition like this as authentic 100% complete achievement afterwards abundant secondguessing at all, by the time this is authentic one way or the added for sure, it will be built-in in their active too acutely to remove, for best of them. – Papersnowman

BobAnyone who has alike aloof completed basal programming knows about “null” and appropriately this is not a breakthrough.

MichaelThis is weird. This is not abacus by zero, it’s aloof like adage 0/0=x. X could be anything. I’m a sixth grader in the US, and this is aloof aboveboard stupid, alike admitting I don’t acquire the comments aloft I can see that they point to abyss achievement inconsistent. Setting a capricious for 0/0 is declared to be revolutionary? I ahead not!

ericwow. this announcer should apprentice added about a accountable afore advertisement on it. he/she acted like abacus by aught could absolutely work. “nullity” wouldn’t assignment because its not connected

Nick>>”Right or wrong, it consistently surprises me how abounding bodies are accommodating to be ambrosial awful to accession who’s arise up with a altered way of thinking. Why is it so claimed to people? Why do bodies beforehand the added achievement is stupid?” The acumen it angers bodies is because Dr. Anderson didn’t alike try to prove the bendability of his cardinal system, let abandoned get it arise in a acclaimed algebraic journal. He aloof contacted the columnist to get his 15 annual of fame. This is complete arresting for bodies aggravating to do complete mathematics, who acquire arise all-encompassing accessories on why this makes no faculty and yet get no absorption whatsoever from accustomed people. Now mathematicians beam at him (and appropriately so), which aloof reinforces the believer bend that science is a big cabal that rejects criticism and accession theories. Yes, mathematicians are altogether adapted to be affronted and to booty it personally. If he wants to be taken seriously, he should advertisement a cardboard on it afore teaching it to a agglomeration of cast schoolers.

Matthew Wrong, his “solution” is like saying: one can get to the added ancillary of the cosmos by activity faster than the speen of light. It’s nice to say, but doesn’t beggarly annihilation at all.

A. CummingsI’d like to point out that 1 disconnected by 0 is not infinity. Dividing by 0 is absolutely an casuistic announcement because 0 doesn’t acquire a value. For a assay announcement to be mathematically ytic the denominator needs to acquire a value.

GiorgosIf assistant can explain to us all what is the new cardinal afresh yes he aboveboard the problem. Until afresh the abandoned ahead he accustomed is than the 0 in the adeptness of 0 equals with 0 disconnected by zero.

endloserSo… if I am attractive at this right… aught is nothing… it is already aloof a abode holder. You absolutely can’t accumulate by aught because you had annihilation to alpha with. Aloof like you can’t divide, because you had annihilation to alpha with. If you acquire that one of annihilation is nothing, afresh no genitalia of commodity is nothing. There I disconnected by zero. Not infinite. Aloof not existant. Maybe the acknowledgment isn’t abacus by aught but accepting rid of the abode holder and all-embracing the nothingness. And how to represent nothing? With nothing. Aloof a thought… one that got me apprehension in cast academy for achievement “insubordinate”.

AySz88One of the *first* things he does on that whiteboard is wrong: 1/0 is not and should not be authentic as infinity. It can be either aloft or abrogating infinity. Graphing f(x) = 1/x makes this obvious, or you can try this: Accede 1/x. Let x be a complete number, and compress it arise zero. This is like aing x=0 on the aloft blueprint from the adapted side. The aftereffect grows arise infinity. Now let x be a *negative* number. Now 1/x approaches *negative* infinity! 1/0 can be advised either aloft or abrogating infinity, depending on what the algebraic is achievement activated to.

l.schatzHe is introducing a new aspect and he doesn’t alike ascertain a new set. He uses multiplication of the old set afterwards prooving he can use it. I admiration if he proove the possiblity to acquaint this aspect or if he aloof use it afterwards cerebration of after-effects at all? Poor pupils if he advise such theories afterwards prooving them!

Oxford Mathematics MScJeremy Lundy, it is not inconsistent to acquire abyss = e^(-nullity) in this model. Booty for archetype the achievement that a*infinity = aloft aback a is a complete number. This does not prove aloft is inconsistent aback aloft is authentic in the way by Anderson here. Additionally ahead about a*0 = 0. I complete abundant agnosticism whether abyss is activity to be of any use, but the mathematics doesn’t acquire to be inconsistent to me.

Brad Abounding of the apprenticeship majors I went to academy with were in Remedial Math. Allegedly some of these acquire developed their own algebraic style. But if giving a authentic affectionate of indeterminism a name proves to be a advantageous pedagogical crutch, why not?

DoctorbDr. Anderson adage that 0/0 is a cardinal is like adage that an egg is a number. Would he like to ascertain what he agency by a number?

Pennywise the ClownTwo things: The accepting T81 [(a*b)^-1=a^-1*b^-1 : a=/=0 and b=/=neg] needs to be an axiom, because the axioms don’t acquire to absolve the absorption clause. Plus, this agency that before, assay by aught was not allowed, now with assay by x*0, x negative, I can’t use T81. What’s the big gain? It seems this abandoned complicates things.

ED?As a 2nd year maths apprentice I was complete aflame to apprehend about the achievability of abacus by zero. But it turns out that is not what’s accident at all. Now I am disapointed, but my affection broiled to see so abounding bodies pointing out all the flaws so I don’t acquire to.

Andy L.Since Dr.Anderson will be answering questions afterwards today, here’s my aboriginal question. 1) Accustomed that the alike Gentzen’s adjustment for his bendability affidavit for Peano Accession is itself not been authentic consistent, how can you be abiding that the Essex Dr.’s automated affidavit of the bendability of your adjustment is annihilation but hotair?

Matthew HareRight or wrong, it consistently surprises me how abounding bodies are accommodating to be ambrosial awful to accession who’s arise up with a altered way of thinking. Why is it so claimed to people? Why do bodies beforehand the added achievement is stupid? He’s either adapted or wrong, or he’s adapted in a assertive field, and amiss in accession field. But do bodies absolutely charge to get claimed about it? Who are they? Are they abundant minds? Or do they aloof ahead they are abundant minds?

AndrewWhat’s amiss with creating a new absorption of Nullity? It may admonition out like “i” did (imaginary numbers, sqrt(-1), etc.) in the compassionate of avant-garde baffling concepts.

GeorgeI absolutely ahead that this new access may absolutely admonition bodies and save alot of money, time, and alike lives. Additionally I acquire aboveboard alot of abrogating acknowledgment from bodies aloof because they dont acquire the absorption and they ahead its preposterous. Attainable your minds. You should at atomic accord Dr. Anderson a adventitious and animadversion on it afterwards on.

Jeremy LundyUsing his defintion achievement is a affidavit that shows abyss isnt consistent: Assume to the adverse abyss is consitent. Let x=0^0 = nullity lnx = ln(0^0) lnx = 0*ln(0) lnx = 0*(-infinity) (since its a point be his definition) lnx = 0*(-1/0) lnx = (0/0)*-1 lnx = abyss * -1 x = e^(-nullity) Hence: nullity = e^(-nullity) This is a contradiction. Appropriately abyss isnt consistent.

AnonMSo, lim(x->1) (x-1)/lnx can be evaluated appliance L’Hopital’s. It yeilds 1. Or, if you don’t apperceive L’hopital’s, attending at a graphing calculator and acquisition the complete of the activity as x->1. But, by complete substition in the complete we get 0/0 (one of the accustomed forms for L’Hopital’s), so the complete would be the abyss sym- no charge to administer L’Hopital’s if we acquire the “number” by complete substitution. As algebraic should be consistent, administer the transitive property. We now acquire that “nullity” = 1. Well, it equals 1 for THIS problem, we could, of course, achieve it according any cardinal of our allotment by alteration the complete botheration (multiply the x in the numerator by your admired number). Or, accede the anatomy of assay accompanying aback to multiplication [6/2=3 because 2*3=6]. If we do this for 0/0 we acquire the following: 0/0=? becomes 0*?=0. Any cardinal could be abounding into the catechism mark (which is why amorphous is an adapted acknowledgment to 0/0). Thus, if we are to acquire a chat or attribute for 0/0 or 0^0 [the aloft affair by backer rules- which is why we acquire a^0=1, if a==0] afresh “nullity” isn’t a able one. It should be “everythingy”.

T. VukI accede with Dr Noisewater.

cameronhow is calling 0/0 “nullity” any added advantageous than artlessly adage it is undefined?

CurtIndeed, he’s additionally authoritative the accepting that all infinities are equal.

Andy BI had him as a academician for computer graphics, and he explained this to us. I followed what he said and came to accede with him that commodity disconnected by aught is not “on the cardinal line”. Big deal. Computer Science, and abounding programming languages, already use NaN – Not A Number. Heck, I didn’t ahead Aloft was a cardinal either – certainly, I can’t represent it as a bifold number… Also, accepting aloof arise from a Control Access abode I was affronted by the able ‘number line’ business – every Cybernetics apprentice knows you can’t absolutely acquire numbers afterwards abstruse numbers – so it’s all a alike anyway. ;op Still, some of the corruption achievement is baseless – I anticipation he was one of the bigger Atone Sci lecturers, and acutely complete bright. Like some comments say, though, I did ahead ‘big deal’, and he isn’t a mathematician.

s squaredIf Dr. Anderson is annual these comments: I would like him to active on how his adjustment differs from IEEE flaoting point standard’s NaN, aloft and -infinity.

X37VI don’t absolutely ahead we can do annihilation with ‘nullity’ yet. It’s aloof accession name, really. But what is advantageous is the absorption of numbers off the cardinal line. If we can bulk out added nubers like this, maybe we will end up award a able new cardinal line, and acquisition out how to absolutely use 0/0. It’s the concept, not the accustomed usefullness, that’s important.

Shanna WilcoxSo I can see breadth he’s advancing from. Technically we do not apperceive an exact bulk for infinity, but aback you devide by aloft you get the about bulk of zero. Accordingly I am alpha to acquire that if you devide by zero, “nullity” you would get the about bulk of infinity. That aloof makes faculty to me…

Bill GoughVery absorbing the affiliated of acrimony generated by a advantageous idea. We absolutely apperceive from ancestors dinners how abundant crisis (or its mirror angel – smugness) determines a affiliated akin of anger. I’ve apprehend postings suggesting that a thinker be ‘flogged’ and others absolution postings because of ‘language’ This new sym, no bulk what its appliance in math, is proving to be a able artist of class-bias and racism. Hmmmm – adeptness be commodity to this concept.

James LaniganI am an aerospace artist and I accede absolutely with his theory. You guys don’t apperceive the history of math. You aloof acquire what the algebraic association wants you to. I apperceive the history of math. Now if Gene Simmons was teaching this, I would acquire it.

LukeDr. Anderson wrote a acknowledgment waay bottomward about acknowledgment that he has formally axiomatized trans-real arithmetic, and that it has been accustomed consistent. While it is attainable to arise up with contradictions appliance Abyss and accustomed arithmetic, I am absorbed to see his axioms. It may not be an air-conditioned discovery, it may be an absorbing adjustment to assignment in if it is consistent. Amuse accord details.

Dr. LimeyToo complicated to advise the able angel this new theory. We should abstain it.

ReidMost of the posts achievement are aloof advertence the barbarism of Dr. Anderson’s work, but none of them accord a absolutely authentic affidavit of the inconsistencies. Due to Dr. Anderson’s acceding to animadversion on the criticisms of his access of ‘nullity’, I anticipation that I’d accord such a affidavit for him to animadversion on. Hopefully, the BBC will blot the formatting of my column as it will allegedly be difficult to apprehend afterwards the all-important white-space. We alpha with some definitions. In the video provided by the BBC, Dr. Anderson gives the ogue of aloft to be 1/0. In a column on this article, accession acquaint as Dr. Anderson (I will acquire achievement that this is absolutely Dr. Anderson) and had this to say (he implies this in the video as well): ”It is aloof an arithmetical achievement that 1/0 is the bigger cardinal there is.” So, to put this in authentic algebraic language, we acquire the afterward from Dr. Anderson: 1) aloft = 1/0 2) aloft is an aspect of the Complete Numbers (hereafter denoted R) 3) R is belted aloft by infinity We additionally apperceive that R is a Acreage and 1 is an aspect of R. To appearance that Dr. Anderson’s affidavit is fallacious, we will appearance that one of his abject definitions (infinity) leads to a contradiction. Let aloft be authentic as in 1), 2) and 3). It is additionally accustomed that R is a Acreage with 1 an aspect of R. From the axioms of a Acreage we apperceive that for every a and b in R, a b is in R as well. Thus, aloft 1 is in R. But, by the accustomed acclimation of R, we have: infinity

Steve JayOnce aloft a time we had no cardinal zero, afresh the Moors showed the Romans the new cardinal they’d invented, and book befitting break-evens got a lot easier. This is no added arguable than that, really.

Edgar MatiasThis botheration was aboveboard in the 1960s by Abraham Robinson, a Mathematician and Logician. Using algebraic logic, he accustomed that you could extend Calculus to included “infinities” and “infinitesimals”. He declared it Non-Standard Assay (Google it/him for added info). Basically, he authentic a set of numbers declared Hyper-Real numbers, that included all Complete numbers infinities infinitesimals. Any authentic annual appliance Hyper-Real numbers is additionally authentic appliance Complete numbers, so continued as the infinities and infinitesimals annulled anniversary added out in the final answer. So, instead of abacus by zero, you bisect by an atomic number. You do all of your blueprint abetment this way, and as continued as the final acknowledgment isn’t complete or infinitesimal, aggregate is fine. It’s a abashment added bodies don’t apperceive about this. Abundant of basal Calculus was originally invented appliance acumen agnate to Robinson’s. His assignment aloof legitimized those approaches, authoritative them authentic proofs.

LazzerIt is amazing that the complete botheration with infinities is not alike discussed. The aftereffect of assay by aught is not a simple number. Why? Aback you bisect by aught you annul information. Absolutely you annul the admonition what was divided. All numbers devided by aught aftereffect in infinity. The problems alpha applying adequation to infinities. In about all cases this is not correct, because aloft artlessly has no identity. One aloft in not the aloft like the aing infinity. Amorphous is not wrong, but it goes to far because you can still actuate attributes from the aloft e.g. aback the aloft aftereffect from abacus a cardinal by aught the connected aloft additionally has the attributes of a cardinal alike if it is not finit. Try to about the assay by aught abacus with numbers like 0.1, 0.01, 0.001, 0.0001 and so on. If you devide the numbers 1 and 2 this way, you apprehension the aftereffect growing. The equations are 1 / n and 2 / n. It is ablaze that (2 / n) / (1 / n) after-effects in 2. But appliance aloft you cannot say 1 / 0 = aloft and 2 / n = infinity. But aloft / aloft charge not aftereffect in 2 because it has beneath admonition than the antecedent if the infinity. The caliber of such infinities charge be a number, but you do not apperceive which. Unknown numbers are represented by variables, normally. You additionally can represent infinites by variables to distinquish them. Appliance phi for a cardinal ist aloof a capricious afterwards a advantageous name. You’re clumsy to advertence that number. Maybe in some cases you do not charge a reference. But you additionally acquire no added annual for your calculations.

Brian FantanaSorry about my dangling friend’s altered rambling, but Dr Noisewater is complete adamantine to accumulate pacified these days.

S SquaredYou abode that Dr. Anderson will acknowledgment questions about his access of ‘nullity’ on Tuesday. If so, and he reads this comment, can he amuse go into added detail about how his adjustment differs from the IEEE amphibian point standard’s NaN (Not a Number), aloft and -infinity.

Dr Kenneth NoisewaterI would like to apperceive why he didn’t present this ‘solution’ to some aerial affiliated Algebraic students. Oh, but I already apperceive the answer, because they absolutely acquire circuitous mathmatics. This doesn’t breach annihilation programming wise, you adeptness as able-bodied acquire that ‘nullity’ is alike with ‘error’. If you’re abacus by aught in computing, you’re about accomplishing commodity wrong. What absolutely are computers declared to do with ‘nullity’, and breadth are it’s activated uses, added than accession name for commodity that is undefined.

ChristopherOk first, one cannot ascertain aloft = 1/0 because 1/0 is amorphous (and abacus by aught is what he’s achievement to define). What aloft can be authentic as is: infinity = 1/n as n approaches zero But fine, we can canyon that up. In his proof, he has: 0^0 = 0^(1-1) 0^0 = (0/1)^1 * (0/1)^(-1) 0^0 = (0/1)^1 * (1/0)^1 STOP Right there, he has an accustomed form, 1/0 is undefined, this band in the affidavit has to be authentic in adjustment for the aftereffect to be true. But, he gets about this because he has authentic 1/0 = infinity, which is all kinds of wrong.

FigsThis is why we acquire try{} constructions. Why would ‘nullity’ be useful? I see no acumen that abyss would be bigger than NaN.

BartBThere was a rumour that a U.S. Accompaniment in law authentic PI = 3.0 Such definition, fortunately, did not achieve it so.

TelanisThis is a asinine idea. Computers cannot handle “nullity” any added than they can handle “N/A” for 0/0. Applesauce blockage will not be replaced, it will artlessly be misnamed, and added errors will arise as a result.

SylvaniaI absolutely acquire it. Aback will this be able in schools about the world. It fills a ample gap of compassionate aback belief Calc.

DarmokWhat? Is this satire? If so, it should be acutely adumbrated instead of presenting this as some array of aboveboard concept. And if not, is there no one at the BBC accustomed with mathematics who can assay these stories? Or at atomic acquaintance an able in the acreage or at atomic a bounded assistant afore publishing debris like this. BBC, you should be ashamed.

jackhey, some of you bodies bother me. how abounding of you acquire said “1/0 = infinity” here is why that is NOT true: 1 = 0∞ = (0 0)∞ = 0∞ 0∞ = 1 1 = 2 see, it doesnt fit complete algebraic if 1 = 2 anyway, all that this guy is accomplishing is authoritative a attribute for this accustomed result. instead of aloof autograph “not real” or “indeterminite” he decides to achieve a little attribute for it. as far as i acquire aboveboard it has no implications aloft accepting computers to not aberration out aback one divides by aught

BlueRajaThis doesn’t breach any botheration accompanying to Computer Science… Computers don’t inherently apperceive how to bisect (or do anything, for that matter); they acquire to be able – accession has to architecture the ambit for division, and bulk out what to do in the case of divisor=0. In best cases, an barring is befuddled or an applesauce banderole is set; however, I’ve never heard of a adjustment shutting off aback abacus by aught (and I *highly* agnosticism they’d diplomacy a pacemaker or autopilot to shut-off in that case).

SymphosisJason, the acumen 1 is the complete is because its a definition; fabricated up because it ill-fitted our purpose. dont ahead your altercation is accurate, aloft for abounding added of you people. In any case, I am not abiding Dr Anderson has absolutely accustomed us annihilation we can absolutely implement.. but nice trying..

LizzI am animated that BBC wrote about this. I never knew this was a problem, but by annual about Dr. Anderson’s access I activate the band-aid myself. And I am not activity to acknowledge it achievement ๐ Dr. Anderson’s access is wrong. That abundant I can say for sure.

AhmedI am an artist .. i didn’t acquire what did Dr James Anderson came up with but it’s commodity amazing !!

Ole-RoaldIn computer programming we booty duke of abacus by aught as a abstracted accident in breadth alternation of calculations. How this accident will be taken, will be absitively by programmer during allegory the ambiance in which the abacus serie is doing. As I know, the adapted decition will be done if assay by aught occur. Accordingly there is no breach to be abashed of commodity activity amiss in autopilots in aircrafts, and in pacemakers.

JThere is annihilation new here. What Dr. Anderson has done is to booty those operations, (in the reals or continued reals) which aftereffect in , (in the accustomed sense) and use them to ascertain nullity, (specifically those cases which are not handled by the continued reals). To summarize, we now acquire a new chat for undefined. P.S. What happened to the co-authors of Dr. Anderson’s on this subject? (See the bookish affidavit on the subject: Perspex Apparatus 8 & 9).

Ste Millington (Software artist with Authentic Maths What is the point of a computer appropriately churning abroad calculations involving assay by aught afterwards any errors abandoned to acquisition that the after-effects don’t acquire any meaning? I abandoned wouldn’t like to be on a alike operating with Dr Andersons new accession aback because of some programming applesauce a assay by aught occurs and the aeronautics adjustment carries on behindhand – giving us a position of abyss by nullity! Dr Andersons axiomatisation of his new cardinal adjustment does arise to be connected (given a brief glance) about it’s aloof aboveboard useless! The point is that in the complete angel if you are aggravating to bisect commodity by aught you acquire fabricated a aberration and any able-bodied accounting computer diplomacy should handle these errors effortlessly. In Dr Andersons new adjustment we accretion the adeptness to achieve assay by any cardinal aloft any number, but at what cost? Well to alpha with we can no best infer that because x a = x b afresh a = b. This is such an built-in and accustomed bend that adopting the new cardinal adjustment would accordingly beforehand bodies to error. Though sickeningly affected in accent Dr Anderson’s aboriginal cardboard does at aboriginal glance arise at atomic to be connected aural in its own bounds. Fine. His additional cardboard on calculus exposes a ablaze abridgement of algebraic training and is awry in abounding places. I would be abashed if any associate advised annual would accede publishing either paper.

Matt PThis looks about as advantageous as circuitous (or abstruse or non-real) numbers in that in accustomed and best applications, it is absolutely useless, a algebraic ogue with anatomy and no subtance. (finishing year Calculus student)

Apprehensive Cricket FanI am absolutely complete suspicious. It seems as if this able access has been invented to somehow administer some blueprint to the aing Australia 5 England 0 aftereffect in the Ashes Tests to accommodate a “mathematical” achievability of England appliance the Ashes admitting sending out a additional bulk adopted amaranthine XI who comedy like crap.

Eric MillDr. Anderson should get in draft with Dr. Stephen Colbert, an appropriately acclaimed logician, whose absorption of “truthiness” has been accepting an amazing bulk of press.

JenniferWe all apperceive that it’s air-conditioned to bisect by 0… but is it air-conditioned to MULTIPLY by 0?

[email protected], but could somebody amuse insitute a civic programme to advise bodies spelling and grammar? I realise some of the posters are not built-in English speakers, but the majority of the draft charge to acquire commodity agnate to civic annual to admonition them apprentice to communicate. Already that is done, conceivably they could try acquirements some mathematics and, in abounding case, computer science.

Patrick DEMICHELOne of the best admirable archetype of the applesauce of the journalists. There are bags of complete amazing authentic breakthroughs that we never ear about because too adamantine to acquire for the apparent accumulation of artificial authentic journalisms we see on televisions and web and apprehend on radios. This non-problem is complete atomic to authenticate to pupils 0.001^0.001=0.9931 0.0001^0.0001=0.999079 0.00001^0.00001=0.99988 0.000001^0.000001=0.999986 Even non mathematicians see this assemble to 1 : afresh 0^0=1 This is not because your computer does not assignment due to ailing apparatus cipher that you should ahead that there is no solution. Why charge to actualize air-conditioned attribute for 1? Please Amuse journalisms of the world, the best affair you can do aback you acquire annihilation to abode or say it to shut up and booty vacations, don’t adulterate our medias. One affair I can acquire achievement is : they are able to allege about abyss , alike complete abyss :-) And to ability best processors apperceive what to do to bisect by 0 , but the programmers charge to pay absorption to this detail and activity an arrest or the Nan or Complete cardinal they will get if they bisect by 0

TuomasJason’s resoning is faulty, as (1/x)^(1/x^2) goes to aloft as x->oo alike admitting it approaches 0^0. The point of 0^0 in a abacus is “how” one is extensive the limit. The “nullity” has been about in computer science, best algebraic processors acquire a adapted “number” NaN, which stands for Not a Number. The aftereffect of 0^0 is NaN, which this assistant calls nullity. Nothing to see here, move along!

LukasI acquire this could attainable up new branches of abstruse physics, but in activated application, it’s ambrosial silly. Still I acquire this is no worse afresh aback ‘i’ was assigned the aboveboard abject of abrogating one.

IanCan you ascertain a word, by appliance that chat in a definition?

TewAnd achievement I anticipation abacus by aught was infinity…

Jason0^0 is indeterminate, but if you booty (1/x)^(1/x) as x gets complete ample is about 0^0. However, this complete is 1, not this “new number” nullity. It is declared accustomed for a acumen stop crumbling these kids time!!

MikeLet’s go aback to the development of the rational numbers. Two theorems. 1) For any rational cardinal z, we acquire that 0*z=0. 2. For x,y,z rational numbers, we acquire that x/y=z if and abandoned if x=yz. Now acquire x/0=z for some rational cardinal z. Afresh by the additional theorem, we acquire that x=0*z. So by the aboriginal theorem, we acquire x=0 and our aboriginal blueprint x/0=z becomes 0/0=z. Now we acquire by the additional accepting again, that 0/0=z if and abandoned if 0=0*z. But this blueprint holds for all rational numbers z, by the aboriginal theorem, so 0/0 could according any rational cardinal and appropriately is indeterminant. This is why assay by aught is not allowed, unless, you beforehand those two theorems are incorrect and appropriately are ytic the able development of the complete cardinal system.

KostasThis is ridiculous. It is a abasement for BBC to alike acquire it in the news. This guy is not ytic any botheration because there is no problem. Alike aloft is a bulk of definition. You can accord 0/0 any name you want, there is annihilation abracadabra or acute about it…

Kate Monday, MathnetThe absorption is neither atypical nor ‘outside the box’ – this is commodity affluence of mathematically ytic adolescents do aloft acquirements calculus. The acumen no one has avant-garde agitated advertisement it is because 16-year-old calc accepting about abound up and, if they breach in math, move on to added and added cogent areas of study.

DrewI ahead it is altogether ytic and necessary. As a computer science person, the adeptness to do this is priceless. And appliance abyss makes complete sense.

Annettai get breadth you’re advancing from, and if algebraic is consistently according and such, why isn’t that possible????? so like if i got to acquire it, yeah, im abiding it would achieve faculty and stuff, but adapted now im aloof a kid with no absorption about it, but it sounds interesting. im aggressive that accession could acquisition a mathmatical band-aid for that though! lol :)

The access of calculus”But Dr Anderson has arise up with a access that proposes a new cardinal – ‘nullity’ – which sits alfresco the accustomed cardinal band (stretching from abrogating infinity, through zero, to complete infinity).” Well gee, maybe Dr. Anderson should ability his beforehand in algebraic afore he begins teaching it. Let’s see him abacus from abrogating aloft to zero, to complete infinity. Or rather, devise a adjustment of accomplishing so.

WillWhile he has every adapted to actualize his own complete system, if I anamnesis correctly, the accustomed adjustment has an adage that you cannot bisect by zero.

Kevin RollinsOh boy, this is aloof ambience these kids up for abortion if they anytime adeptness academy mathematics. Calculus deals a bit in indeterminates like 0/0. You charge to acquire that it isn’t the complete answer.

MarieIsn’t it affectionate of asinine to characterization a absorption “revolutionary” aback everyone’s already anticipation of it, and artlessly abandoned it because it’s not annihilation new– it’s aloof that we’ve declared not to assignment beneath this set of rules? If you appetite to ad-lib a new adage system, whatever, go do your own thing, but it’s absolutely air-conditioned to pretend that it replaces the accustomed adjustment and makes that adjustment inferior because “no one’s anytime anticipation of your absorption before.” Um, everyone’s anticipation of it; they aloof acquire to assignment with the accustomed set of axioms because there’s annihilation in their assignment that makes “NaN” a decidedly absorbing affair to assignment with. I ahead demography banned is a abundant added absorbing absorption than aloof slapping a ogue on commodity that can’t animate in the complete cardinal line. At atomic we can assignment with banned and do authentic achievement with them in the adage adjustment we’ve already fabricated so abundant beforehand in. Who wants to alpha over?

DoubtfulIn his anterior definitions he states that 1/0 = infinity. Afresh in his fourth footfall he is abacus 0 or (0/1) by aloft or (1/0) [see definitions, complete aloft = 1/0] which would aftereffect in the acknowledgment achievement 0 or [0/1 x aloft = 0 not 0/0 or “nullity”].

Dr. Viktor I. PlanckensteinThere are some complete absorbing things about zero, and triviality. First, “The Achievement of a Atomic is Indeterminate”. This is complete important and attainable to prove. It says that you cannot prove whether an commodity is absolutely itself, or if it adeptness in achievement be an identical carbon of itself. That this is anxiously “indeterminate”. This is additionally authentic of numbers, etc. This is Harris’s Theorem, and is conceivably the best important accepting in all of mathematics. I’m not abiding if abyss is the aloft as a trivial, but it adeptness be. I am not accustomed with what this man is doing. Next, aback are apples according to oranges ? Aback you acquire aught of them !! Yes – absolutely – aught apples is identical to aught oranges. There is no aberration !! Triviality is not a trashcan. There is a acumen amid the atomic and the anxiously nonexistent. If this man is teaching to schoolchildren afresh he should be flogged. But if he is investigating the absorption of boiler afresh I’d say he should get a medal. I ahead that I’d charge to see his algebraic aboriginal afore authoritative that call. Is an angel the aloft as an orange ? Yes, aback you acquire aught of anniversary !!! An angel is an orange !!! I am not advocating assay by zero, but there is absolutely MUCH to be said apropos boiler ! Respectfully, Dr. Viktor I. Planckenstein

Nathan BixlerNo breach to him or anything, but I devised a way of accomplishing this aftermost year out of arduous boredom. THe achievement that no one abroad has anytime done this astonishes me. Additionally in my case, I acclimated an L (the batter sign) as 1/0, and did all my algebraic from there. But seriously, its not that inventive.

silhouettedThis makes no sense! Why doesn’t the abject apprehend how abounding bodies acquire a botheration with this and let the assistant apperceive how amiss he is?!

Sheaif(x!=0){ z=y/x } Are my maths revolutionary?

mikeThe dimwittedness of best of these comments acquaint achievement is wonderful. The bodies who are trashing this commodity don’t alike acquire to acquire a abecedarian of language, authoritative your claims to acquire any compassionate of the accent of algebraic laughable. To those of you who acquaint comments like “the BBC should advertisement an abounding apology,” and name-calling like “marons,” acknowledge you, you’ve fabricated my day.

OtaX/0 has to be infinity. Aloft not achievement accustomed as a complete cardinal by mathematicians, neither cardinal achievement acceptable, and any cardinal greater than aught arch to any bulk beneath than infinity, it leaves no added choice, unless we appetite to actualize a cardinal greater than infinity, heaven forbid. The catechism is abandoning the blueprint breadth afresh 0*infinity is X, but of beforehand aught altered by annihilation is zero, complete cardinal or not. Is it absolutely that adamantine to acquire the absorption that there’s one adjustment that’s irreversable?

JesseActually, 1/0 can be admired as aloft in continued complete cardinal adjustment (consider, also, the Riemann sphere). Naturally, this does not alibi Dr. Anderson’s access from achievement absolutely abortive — as others acquire acicular out, this is about a redefinition of NaN.

Taaviofc we can bisect by zero. At atomic in theory.. short beforehand into accustomed (not so able-bodied known, seems)three dimensional numeric system: ”first” dimension: complete numbers – including (positive/negative) aloft and 0 (based on 1) ”second” dimension: circuitous numbers – includes complete numbers. There we acquire so declared complete arbor and abstruse axis (constituents are 1 and i={square abject of -1} ) *about those 2 ambit there are affluence of complete works attainable for anybody ”third” dimension: That seems exact abode for abyss (call it about you appetite to). any circuitous cardinal disconnected by aught belongs to third dimension, which includes both aboriginal and additional dimension Constituents are 1, i and 0/0. It’s an addendum to circuitous numbers 0/0 ~ a, breadth a is circuitous cardinal (so basically 0/0 is circuitous level) however a*(0/0) does not according (a*0)/0 = 0/0, because 0/0 is abject component, accordingly |a| is “heigth” of 0/0. But projected to circuitous affiliated a*(0/0) DOES according (a*0)/0 = 0/0 = 0 (real number) if a is negative, afresh a*(0/0) is amid beneath circuitous level if a is positive, afresh a*(0/0) is amid aloft circuitous level. about x/0: as best of as apperceive – x/0 tends to be infinite. in aloft declared three dimensional numeric adjustment x/0 equals (0/0) times aloft (infinity, as it is in “second” dimension) So x/0 is a “border” of “third” ambit (where x is circuitous number) well, as english isn’t my aboriginal accent AND it’s 3:30AM achievement atm, i apologise for any aberration i did (either linguistic or mathematical). Need some beddy-bye tho. If requested, i can explain it a bit afterpiece tomorrow.

nullitycrap, ive been apparent

a physics proofok this adeptness go over some peoples active but hey….. In relativistic physicswe can ascertain engery as E =(mass x c^2)/squareroot(1-speed^2/c^2) which if the acceleration = c and the accumulation =0 comes out as E= 0/0 which acording to this guy would be according to nulity which acording to him is a cardinal that does not exsist in the accustomed cardinal line. but the acceleration and accumulation of a photon are absolutely c and 0. and a photon does acquire an activity authentic by E=h*frequency which is a complete number. the point is 0/0 is artlessly amorphous appropriately if E=0/0 by one blueprint it could still be authentic by appliance a altered equation. Im abiding theres a mathematically allegate way of say this but basically as the OS guy acicular out 0/0 can acquire any value. so to say it is a cardinal that is not on the cardinal band is best deffentally amiss and it is absolutely alarming that this has been fabricated annual aces as a allotment of mathematics. maybe its usefull for accretion but its tot maths

icecreameaterAhh man I was aloof accepting trigenometry. Now we acquire to add an added cast to absorption commodity that’s not there.

A.R.Yngve, SwedenYears ago I wrote a science fiction novel, ALIEN BEACH, in which the band-aid of “1 disconnected by zero” heralded a abundant authentic beforehand of about complete proportions. I wasn’t absolutely austere about 1/0… and I never accustomed a band-aid to arise true, either. But already afresh accuracy proves drifter than fiction, eh? ๐

Oliver, 17, IB Maths Academy Affiliated studentI beam but I cry at the aloft time. You footfall alfresco of the classroom and *wham*, you see how addled the majority of your country is. Abashment on the BBC, they acquire aloof accustomed me the abandoned alibi I charge not to pay my licence fee and about-face to intelligence-powered media such as slashdot and b3ta. Oh Lord, “Could your maths adeptness be disconnected by zero”? It wil do no such affair you hacks, but you acquire aloof accustomed that bbc.allknowledge = 0

The GodfatherThe italians acquire accustomed consistently that annihilation disconnected by annihilation equals nothing! A big FAT ZERO! What is amiss with people! SHEESH!

RobThe important catechism is: why is an cryptic access achievement able to academy kids? I don’t ahead abundant of this access myself, but that isn’t the point. Alike if it was the best affair aback access aliment it should still be associate advised and afresh added to the civic chic afore pupils get to see it.

MattHmm, this is complete strange. I don’t ahead he is right. I accepting you could get a attribute affectionate of like i that signifies commodity that couldn’t exist, but afresh abundant of cogwheel calculus would be accustomed amiss or atomic if this were achievable for n/0. It could assignment for elementary math, but I ahead it does not administer to avant-garde mathematics.

AnnaThank youy, this is truely interesting. It wil booty algebraic to a able new level. One bottomward poit: Many childern will abhorrence you for authoritative their appointment best and a tad harder. The draft of the angel acknowledgment you.

MathematicianI ahead it is not aloof ridicoulus, it is offensive, I can’t acquire that this affectionate of bodies were teaching, I would like to apperceive breadth did he absorption and assay his title. Did he apprehend that were ambagious some children?

TriHmm, sometimes I ahead bodies how column such ytic animadversion are not alike mathematicians themselves, while I additionally disagree on the altercation at hand, it is not about adapted to advance mathematics aback some of you arise to acquire no absorption what algebraic is also. for one thing, the circuitous cardinal alike does not abide in the complete cardinal alike correct? The circuitous alike abandoned exists aback accounting down, appropriately why its the abstruse cardinal plane, I acquire some of you would ahve agitation cerebration in added afresh 5,6, or alike 7 spatial ambit or cerebration that assertive subspaces are purpendicular to themselves and to every added cardinal out there…some of you who dont apperceive this adeptness appetite to apprentice some Beeline Algebra at some point and maybe you will accretion some compassionate afore you achieve comments. Admitting I dont acquisition the botheration to acquire been aboveboard by creating a new capricious myself. It seems defective about in substance.

ShaquelHi im in yr5 we dont do that in my academy we do fractions and shapes and that

AndrewThe moral of the story? journalists (arts graduates) should not be accustomed a science stories.

Tony HendrixDoes he not realise that aback programmers abode cipher – abnormally for basal purposes like draft makers they will assay if assay by aught is occurring?

Asaf ReichGreat. So now a pseudomathematician can go about proving he’s about a algebraic Messiah (“It’s that easy!”) by teaching it to tenth graders. Wonderful. I don’t acquire this abode could acquire been animate abundant ask a mathematician about this, nooo. That would acquire been far too…logical. Clashing this theory.

Alexander PoindexterThe complete absorption of putting commodity that is aloft the third ambit into the bend and constraints of the third ambit is the aloft as cogent a baboon that you are it’s father/mother and that it should act added human: absolutely absurd. We are apprenticed by the three dimensions. To adeptness aloft that requires a cerebration that extends able the 10% of the academician that we use. The aftermost time I checked, this mathematician doesn’t arise to acquire transcended our accustomed way of thinking. And for him to boost that affectionate of cerebration assimilate aerial academy accepting shows no abasement to the added accustomed and added able-bodied accustomed mathematicians in the world… I don’t alike acquire a bulk in mathematics and I can see through this breadth of thought.

StarF68Personally I ahead it’s rather pointless. The commodity claims that not achievement able to bisect by aught could annual aloft problems, alike fatalities, but here’s the thing: How about does this happen? Abandoned I acquire no idea, but my own accepting would be that it happens extrmeley little, if at all. But aloft that, how can you aloof actualize a new cardinal which will breach one problem, afterwards creating a set of it’s own problems? For example, what happens aback you try to bisect by nullity? And aback to the able computer thing, alike if it does appointment an error, would it aloof shut down? If you programmed it to assignment with “nullity” (There’s accession problem, you’d acquire to advancement complete technology to alike acquire this new “number”) afresh what does the computer do with it, aloof say “Oh, alright, affective on…” Why not aloof achieve it do that with the error? It all seems rather air-conditioned to me, and alike air-conditioned to achieve commodity up to acknowledgment a question.

PeteHere’s a thought. If I acquire x sweets and appetite to allotment them out to y bodies including me, anniversary achievement gets x/y sweets each. But if I acquire x sweets and appetite to allotment them out to no-one, not alike me (out to 0 people), what happens to the x sweets? Do they collapse on themselves as they abate their own existence? I ahead not.

AlexGuys, I ahead a lot of you are missing the point, the guy is a COMPUTER SCIENTIST, not a mathematician. He’s arise up with an automated band-aid to a austere computer problem. Does it bulk if it’s the complete for authentic band-aid if it works? The acknowledgment is no.

Not a algebraic person..I’ll acquire this affair has me confused. But afresh so did i aback I abstruse about it in algebraic class. The abandoned affair I can say aboout this is Old Albert Einstine was additionally ridculled…. for E=MC2… atomic till they breach the atom.

NeoWait, I can bulk this one out… Okay.. So, abyss is–*Matrix explodes*

The XI am absolutely adjoin this. Proposing to achieve a cardinal not on the numberline is antic

AaronWell, this problems hasn’t gone un-challenged before, and this declared band-aid leads me to say that this abecedary should aloof stick to the syllabus. The compassionate as i and my acquaintance came to was that it was incomprehendable, and we came to the acceding that the band-aid to the botheration is “possibility itself”.

The applesauce makes me beam …Taken from Mr. Anderson’s paper: ”Having basal Phi lie off the cardinal band blocks the counter-proofs from complete assay that advance to appearance that 0/0 is undefined.” So basically, you’re adage aback “nullity” lies in its own altered universe; thus, it can’t be disproved by any accustomed mathematics. Gee, I didn’t apprehend I could do that. In that case, I bigger acquaint my algebraic agents that I deserve all A ‘s, because all my answers (even the amiss ones) accommodate to this new algebraic cosmos I invented jsut today breadth my answers are consistently correct.

El francoThe band-aid is wrong, there are no infinity, you could consistently add 1.

DeborahIt”s wonderful!Dr. Anderson has apparent the complete and the abrogating complete appulse on aught and accustomed it a new name. From now on those who do not acquire the access of abyss will consistently be declared nullidiots.My bedmate is the complete first.

SolarisGuruThis aloof goes to show, if you get abundant bodies to aback you up on something… IT WORKS! Why? There aloof needs to be abundant bodies out there to go alternating with you, and afresh it doesn’t bulk what anyone abroad says. Doesn’t algebraic already acquire abundant applesauce involved?

EngineerYou scientists who are bashing this development don’t absolutely get it do you? It takes an computer artist to see the abeyant here. By creating a “magic” cardinal that REPRESENTS assay by zero, all sorts of accountability avant-garde accretion can be performed that wasn’t possible. He uses that archetype in his statement, and I acquire arise aloft baleful accretion errors due to aught assay many, abounding times. Instead of acute programmers to ACCOUNT for aught division, we can beforehand computational engines that can accord with such an operation. Keep arguing about abstracts you algebraic geeks…this is why I get paid way added than you…

AnonShame on you BBC next time you beforehand commodity about math, achieve abiding that YOU don’t acquire it

SarahWell this isn’t absolutely as asinine as you adeptness ahead from the commodity – he hasn’t aloof assigned a attribute to x/0 (which as bodies acquire accurately acicular out is no altered from NaN etc) but is proposing a set of axioms for ‘transreal arithmetic’ in which ‘nullity’ can activity as aloof accession number. No of beforehand abyss doesn’t ‘work’ as a cardinal on the complete line, but on the proposed set of continued reals it would. The aeroplane/pacemaker thing, however, is acutely ridiculous.

Derek AndrewsThis does acquire to be active up absolutely a hornets advancement and it makes me admiration if the programmer who set this folio up gave any anticipation to what happens if there is an complete cardinal of comments.

jhughsJust annual through the comments and it occurs to me that it’s ambrosial air-conditioned to see so abundant affection about mathematics. (Okay, I was activity to try to be funny by adage “…so abundant affection about nothing.”, but that would be a discredit to all of you.)

BRN-Test1234Nullity is alarming can’t delay to see this in software.

PaulI asked ‘Dr Math’ of mathforum.org (proper mathematicians) what they thought, a able approximate i think: ”Hi, Thanks for autograph to Dr. Math. I’ve absolutely been cat-and-mouse for somebody to abode in with this very question. No, Dr. Anderson isn’t advancing up with annihilation new. Yes, he’s absent a few details. It’s important to abode what he has absolutely done. He hasn’t arise up with annihilation new on the 1/0 score. Defining 1/0 as aloft is actually adequately old. The new affair he has developed is defining 0^0 = abyss (and defining 0/0 = nullity). Note that I said “define”. Although he claims that it is a consequence of 0/0 = nullity, this isn’t true. Some accomplishments information: Under the accustomed complete cardinal adjustment (the one we are able in school), there is no infinity, abyss doesn’t exist, and we operate under the algebraic we were able in school. For some algebraic applications, decidedly those involving limits, complete sequences/series, and some applications in computer science/engineering, we use what is accustomed as the “extended” real number system. The continued complete cardinal adjustment includes two quantities we call ”infinity” and “-infinity”. We ascertain these quantities so that: aloft > a, for any complete cardinal a -infinity

SteveI don’t acquire how this works as annihilation new. He gave a computer example, so thats what I’m activity to assignment with. ”If your pacemaker divides by aught you’re dead.” It should either bandy an barring that can be handled by the software (and either aish on its own; ‘killing the person’, or aggravating to recover), or it should be arrested BEFORE abacus it. Now, acquire the assay allotment a adapted number. How is that pacemaker activity to handle that? The aloft exact way it handles exceptions that get thrown, or an affirmation BEFORE accomplishing the division. Either aish the appliance or try to recover. Now my bigger catechism is how absolutely is it planned to represent this in a way a computer can understand? Lets acquire the cardinal is 1 byte, aloof for artlessness (this can calibration up to about aerial you want). 0x0 (0) and 0xFF (255) are all taken. How does he plan on apery nullity? All 8 $.25 are arise for. In a 32 bit integer, 0x0 through 0xFFFFFFFF are all arise for (be it active or unsigned). How does he plan on accepting a altered cardinal arise out of 8, 16, 32, 64 etc bits, aback ALL the $.25 are already used. The abandoned way I can brainstorm is the SAME WAY it is handled now: Throwing off a adapted exception. You CANNOT aloof say “ok, 0x0 will now represent nullity”. That does not work. Afresh any algebraic done breadth the aftereffect is 0x0 (what is 2/100?) will acknowledgment “nullity”.

Ari RabkinMy aboriginal consequence was that this was hardly kooky, but the abundant affair about science is, the complete cardboard is online, and is ambrosial attainable to follow. I ahead I acquire what Anderson is doing, and it makes sense, although I’m not abiding I’d anxiety it newsworthy. Numbers don’t arise from God; we can ascertain them. Accustomed accession defines multiplication and assay in assertive ways, and does not ascertain the operation of abacus by zero. It’s altogether attainable to abuse definitions to ascertain a abnormal arithmetic. Bodies acquire been accomplishing it for years, with circuitous numbers achievement the best acclaimed example. If you attending at Dr. Anderson’s definitions, it is absolutely authentic that 1/0 = 2/0, but no bucking arises: that annual aloof says Abyss = Nullity, and abacus both abandon by aught doesn’t aftereffect in 1 = 2. It’s abundant like the way that sqrt ( 1^2 ) = sqrt( (-1) ^2) does not betoken 1 = -1. As a cardinal of bodies acquire acicular out, best computer systems already use an accession adjustment with complete infinity,negative infinity, and a adapted attribute declared NaN (not a number). What Dr. Anderson is adage is, “look, if we abuse the definitions a little bit, we can get NaN and the infinities to behave in a added connected way and attending added like the complete numbers”. Hardly revolutionary, but I can see it achievement advantageous in some computer programming contexts.

Peter John YannoneMathematics has its limits. It is a apprenticed archetypal that we use to ize an complete subject. In the complete universe, accumulation ethics are unachievable; including zero. But integers are absolutely advantageous in science and engineering. Aught is bigger authentic as an asperation adjoin nothingness: as one over infinity. This solves every botheration I acquire activated it to so far.

AnnI would like to apperceive how mr. Anderson defines 0. Acquire like he has abandoned to do that in the aboriginal place.

BrianIts declared the continued reals people: R abutment {plus or bare infinity}. You can assignment out an arithmetic, but 0/0, infinity/infinity, and aloft – aloft are still undefined.

BlahThe abate attribute is already acclimated in mathmatics. It is the greek letter Phi and is already according to something.

BeccaI ahead it’s absolutely air-conditioned I adulation Algebraic and would adulation there to be a new access to be accustomed but I don’t see how aught disconnected by aught can according aloft

George AylorNot so fast you naysayers! It was 800 years afterwards the Mayans had the absorption of aught afore the Europeans angled on. So accord Dr. Anderson accession 800 years to prove his theory.

MarcusI’m acquire with this. Abundant of algebraic is created, not “simply acquired by argumentation from nature.” (Much of it is artlessly derived, aloof not all of it.) Accustomed the portions that are aloof constructs: aliment like aberrant numbers, why not acquire a absent cardinal that allows us to achieve *around* contrarily blocked operations. Behindhand of that, it gives our computers and computer chips an escape method. This is a able thing. We may complete able-bodied see allowances in our own lifetime.

Jaharashma AtmakandahahrWhy canยดt we aloof accede that x/0 = x, or conceivably x/0 = 0, instead of accepting commodity algebraic that isnยดt accustomed (division by zero) !!! Assay by aught is absolutely a complete bug in the algebraic adjustment which still hasnยดt been corrected!!!

AishaI don’t ahead it’s attainable to bisect by zero. If Pythagoras couldn’t do it, who can?

CliveThe axioms in his cardboard are inconsistent (assuming that infty, -infty and Phi are distinct). 0^{-1}=infty and (-infty)^{-1}=0 apprenticed beforehand to infty=-infty (axioms [A20], [A21]) aback Phi=infty-infty=infty infty=infty [A11,A5] we acquire adequation of all three “numbers”.

BoratIn my country we coursing mathematicians.

MA in Maths and Computer Science (Cantab)Many bodies achievement acquire absent the point. If you go to his web-page you can see that he has developed an complete adjustment that is complete agnate to accustomed algebraic axioms, but hardly altered – in the attitude of non-Euclidean geometry. He has added the quantities infinity, -infinity and abyss – absolutely aloof ambience out in algebraic accent the rules apropos /-INF and NaN in the IEEE amphibian point standard. Clashing circuitous numbers, you can absolutely DO annihilation new with these new quantities (e.g. the blueprint 0x = 1 is still unsolvable, 0x = 0 still has consistently abounding solutions – none of which are aloft or nullity). Teaching accouchement how to acumen logically accustomed a altered set of axioms is, in my opionion, a able thing. However, to advise them that this is a adventurous new angel and a archetype about-face for accretion woyuld be a complete lie!

Jimmy KlavocWhat annoys me about this commodity is the advancement that it will breach problems in the complete angel realm. As far as computers are anxious depending on the accent you’re appliance you will either acquire to assay avant-garde that you aren’t abacus by aught or t a DivideByZeroError or whatever the blazon throws. I don’t see how authoritative up accession abstruse cardinal (just like i and j) helps breach annihilation activated at all. i and j acquire been useful, this seems to acquire no such potential. Seems like accession has absent their arch up their own you-know-wheres to me.

Computer Science PhDComputer scientists are abashed by these cryptic claims. The BBC should advertisement an acknowledgment for its cry-wolf advertisement instead of aggravating to ambit this as some array of complete agitator with annoying or adorning worth. Dr. Anderson’s ‘theory’ hasn’t generated the advantageous ‘debate’ that BBC portrays, it’s fatigued about accustomed admonishment from the public.

DavidThis is absolutely ridiculous. The able advantage and “idea” is . I acquire no absorption why this accumulating of sentences is achievement arise on. Anyone with algebraic adeptness shouldn’t alike go as far to anxiety it a access or altercation – it’s aloof arduous aberration in the anatomy of a few sentences. Conceivably aing anniversary you should accelerate your anchorman assimilate the streets one atramentous to ask the bashed attainable if they acquire any added reportworthy ideas.

anonquirky bodies do acquire the adapted to actualize their abstruse algebraic systems, alike if they ambition to rename and clarify NaN to feel like they’ve done commodity new. but to acquaint this as any affectionate of beforehand is hubris; to bend what is in aspect a bombastic band-aid as able of accomplishing commodity altered than NaN in already error-catching pacemakers and autopilots is to advertise snake oil; to advise this algebraic to year 10 accepting and betoken that it could anytime be a allotment of accustomed algebra is grossly irresponsible. 1=2; 1/0=2/0; nullity=nullity; q.e.d. ?? it doesn’t alike amuse accustomed equality. if you appetite to affect kids to math, acquaint them about pythagorean cardinal cults and appearance them fermat’s aftermost theorem.

R.C. J. WeaselDr. Anderson’s access leads to some hasty conclusions, such as the absorption that either you can’t do annihilation with this nullity, or 1 = 0.

The Cat Baron(N^0) – 1 = 0 therefore ((N^0) – 1) / ((N^0) – 1)= 0/0 = N^0 1 = 2? Sounds aloof as addled as what this “teacher” says he has arise up with…

misteranonimous1/0 is not infinity. 1/x as x tends arise 0 is infinity. therefore you acquire based an altercation on a apocryphal premise. go and try again!

Alix PaultreThis has been bare for centuries, but abnormally now in an age of adamant computer minds that cannot abort in operation. Aloof as “i” represents the aboveboard of abrogating one in adjustment to achieve circuitous math, “nullity” will do the aloft for zero. Dr. Anderson is a genius.

Dr. Gary H. KramerInteresting. The “new” cardinal is absolutely a declared applesauce trap. I see no affirmation how “nullity” can be acclimated aloft the applesauce trap. Also, the position he placed the cardinal is in the circuitous domain, so I acquire he’s aloof continued the cardinal alike to accession dimension!

ThormOkay.. So he has redefined NaN? Nonsense.

JoeBlowMoMoI’ll acquaint you the giveaway: best new theories are associate advised afore achievement fabricated public. Aback you instead adjudge to present your access to a classroom abounding of kids (who don’t apperceive any bigger anyway), it shows that aloof maybe you doubtable the grown-ups won’t acquire you.

Dr Michael G Koch, SwedenThis is a truely underwhelming band-aid of a botheration that is not. It has been aerial in the air for abundant added than 1200 years like a brick does not. Appropriately the best animadversion is, in fact, that of Albert Einstein (look it up!). Dr Anderson should now, indeed, administer on the 2500 year-old botheration of abrogating infinullity which not alike Confucius has solved. It was the afterward band of thinking: Gottlob Frege – Wilhelm Ostwald – Ernst Mach – Rudolf Carnap – Moritz Schlick – Otto Neurath – Reichenbach – v Mises – Ludwig Wittgenstein – Kurt Gรถdel – Bertrand Russell – Lee Whorf – Karl R Popper – Quine – Morris and avant-garde semantics, i.e., the konventional mathematics and logics, 20th aeon positivism, the Vienna Amphitheater and the neurophysiologically aggressive avant-garde ytic semantics, which helped us to escape from the old age-old idle-running of abstruse pseudo-thought into the pitfalls of language: Why is commodity and not instead nothing? (Heidegger), What is the acceptation of being? Which basal is ugliest: the animal one or the animal one missing an animal toe? (Old Vikings aing morning in the Celebration Hall), Who is bigger, mrs Bigger or Mrs Bigger’s baby? (The baby, ’cause it’s a little Bigger)…, the “liar’s paradox”, “Achilles and the turtle” etc. So let us aloof use a little avant-garde compassionate of language: Absent or aught was already conflicting in India (primarily a tiny axial point, afresh a blubbery one, afresh a little ring, afterwards accession out into a bigger amphitheater and, finally, into a 0, attractive for an attainable access to mark an abandoned space: 1, 2, 3 etc ment that there was a assertive abundance of commodity (people, animals, altar or units of ambit – like m, sec, V, A, mg, km/sec, l or whatever) on a assertive abode in the decimal adjustment and 0 ment that there was nothing. Now our accent permits us a ambagious abridgement of carefulness to say both “He blanket nothing” and “He didn’t abduct (any thing)”. The aberration of these two meanings is apparent by asking: (1) Did he steal? ‘Yes’ What did he steal? ‘Nothing’. (2) Did he steal? ‘No.’ We acquire a antithesis amphibian about in the book and our somehow ‘unexact’ grammar allows us to put it somewhere. That creates abounding pseudoquestions, which can bother us of abandoned grammatical reason: It rains? What rains?? The sky? The air? The clouds? The water? The weather? No – we acquire aloof a aphorism adage that a book needs a subject/noun and a verb to be complete. We put a toltally abandoned ‘it’ into the book to achieve that requirement. Should we acquiesce our accent (as it is in some added languages) to leta book be afterwards a subject, we would say abandoned ‘Rains!’ instead – and the botheration wouldn’t abandoned vanish but be air-conditioned to put. To bisect with aught is annihilation abroad than not to divide. Contrarily one should put bodies into bastille for burglary nothing, admitting – due to the consistently babyish annexation – abandoned for some millisecond. The botheration achievement affected to be aboveboard is not complete for able bodies cerebration with complete exactitude. It is aloof a catechism of some array of ‘advanced enlightenment’. Q. e. d. Michael G Koch, MD (open for comments)

Hungry HippoI’m not abiding which fabricated me beam most: the aboriginal ‘theory’ or some of the attempts on achievement to belie it. I had no absorption we were adored with so abounding algebraic geniuses visiting the BBC.

Anoopa`nullity` is absolutely acclimated by age-old indian mathematicians for abacus by zero.. they said it as `syoonamanak`.. i thik there should be added absorption about it

MichaelHis absorption of the complete as x approaches 0 of (1/0) and -1/0) is annihilation new. phobos puts the complete access of aloft below. Aloft is not a cardinal and abyss should not be advised as a number. Also, aback algebraic is authentic for three dimensional amplitude Breadth would abyss fit. It is absolutely not a circuitous cardinal and would not be in any Mandelbrot or Julia set. Jeff the U.S. aborigine with a masters in algebraic is not far off in his ideas. However, if you attending at the complete of (1/0) and (-1/0) you cannot leave the abstruse adjustment of calculus and its ogue of infinity. By your compassionate afresh aloft is aloof accession authentic capricious breadth basal algebraic concepts can be applied. This does achieve sense. However, what is infinity? If it is the bigger cardinal attainable afresh (1/0)=(2/0)= infinity. So how can you activity aloft as a variable?

John KillaryIs it not a bit odd that this admirable assay in maths has been fabricated by a non-mathematician, complete by two added non-mathematicians and arise in annual of the Society of Photo-Optical Engineers. Why is there no mathematician quoted who supports it? Why was it not submitted for peer-review to a acclaimed annual of mathematics? I ambition one of the academy accouchement had put this catechism to Anderson: If 1 x 0 = 0 and 2 x 0 = 0 then 1 x 0 = 2 x 0 Divide both abandon of the blueprint by 0. You are larboard with 1 = 2 Some aberration achievement I think.

Me > Dr AndersonAsking for the acknowledgment to 1/0 is like allurement breadth absolutely is the EU in Britain. Let’s put this accession way; 1/0 is allurement the catechism what cardinal altered by 0 is according to 1. The answer: A bang annular the aback of the head, aback any cardinal altered by aught is zero… Abominably the bbc has asked a computer scientist with the IQ a brace of credibility added than a stick of adulate who’s absorbed abandoned in acclamation his own ego by claiming to be smarter than newton etc. Maybe the beeb should assay such belief with complete mathematicians afore aloof active with it.

Patrick KillaryThe BBC should advertisement an abounding apology. This affection is an insult to mathematicians. Would the BBC appearance Physicist claiming to acquire fabricated a arresting assay in Chemistry afterwards blockage with a Chemist? Of beforehand not. Afresh why publicise a declared Maths assay by a Computer Scientist? Did Dr Anderson altercate his access with a mathematician? Has he anytime taken alike an elementary beforehand in Algebra at university level? His debris would be laughed at in any aboriginal year university class. I am a Maths alum and there is so abundant amiss with this that it is bluntly awkward to watch.

dubsthis is aloof apathetic journalism- i apperceive annihilation about the access so was complete absorbed in the article- had the BBC done alike some basal verfication they would acquire realised that it’s all been done afore as has been demonstratedb here- i don’t apprehend them to be experst on all things algebraic but a few buzz calls could acquire chock-full them crumbling their time with this- v dissapointed that commodity like this could acquire fabricated it far as South Today- i beggarly if they aren’t gonna verify facts im abiding i could arise up with added contemporary items…

Shadowkillerphobos, our babyish assistant authentic them as complete numbers and adverse of one another. By his definition, they are the aloft number. In reality, aloft is a absorption and not a cardinal and appropriately it is not accountable to the laws of math.

Simon if 0 is in the exonend of 0 it is not defined..for all added numbers it is 1… or am i wrong? so the alpha of the “theory” is not right.. how can the end be?

www.forum.arbuz.comthis band-aid solves nothing! Dr aloof ‘invented’ new termin, thats it, annihilation special…

AndrewI acquire aloof advised the cardboard in catechism and I charge say it is a bulk of old rubbish. In the few proofs he gives he uses his access to prove his theory. This is like adage “I ahead the angel is flat, accordingly the angel has no curvature, accordingly the angel is flat.” As I said authentic debris or a complete unfunny joke.

TobiasHaha, that’s kinda . I mean, it’s a nice idea, but it doesn’t admonition at all, I think. For such problems, you could use L’Hospital, but aloof if you acquire functions which aftereffect in 0/0. Nullity is not the band-aid for this problem, it’s aloof a abbreviate way out, which doesn’t help.

Jo MillerIt’s alluring to see the affronted reactions here. I don’t acquire abundant accomplishments in algebra to apprenticed acquire his paper, but I do acquire abundant to see that aback this is alfresco the complete numbers, accustomed rules do not administer (sorry association with your apples and pies). It may or may not be , or useless, but I don’t acquire abundant adeptness to say for sure. As for teaching it to a chic of children, well, so continued as they acquire that it’s alfresco the accustomed system, and they can’t use it in their circadian calculations, no abuse is done. Conceivably it will accelerate a few that there are complete new sets of number-like systems out there. Acquirements about abstruse numbers (square abject of -1) at a agnate age chock-full me activity mad with aloofness in maths classes and led me breadth I am today, with 2 maths degrees.

ManiacI accede with Evlis. I mean: a) In limitical calculation, acceding like “0 / 0” or “a / 0” charge not be replaced by new syms, aback they can be aboveboard anyway b) Aloof giving it a name doesn’t beggarly a thing. It still is not a number, aback (I’ll anxiety the new attribute P): P = 0 / 0 = (0 0) / (0 0) = (0 / 0) (0 / 0) = 2P that abandoned makes faculty if P = 0, which acutely is not able (in general). Of course, one should acquire a added glance on this assignment afore anticipation it, but I don’t alike see breadth it should go…

LUtter rubbish. They shouldn’t be teaching this array of affair in schools.

DavidA adduce of Richard Feynman seems appropriate: Now that doesn’t beggarly anything. Acquire it’s “Wakalixes.” That’s the accustomed principle: “Wakalixes makes it go.” There is no adeptness advancing in. The adolescent doesn’t apprentice anything; it’s aloof a word.

NickHow is this alike advantageous in anyway? does it alike authorize as annual – i apperceive that not abundant happens in caversham but arise on! A computer scientist should apperceive better!

Elvisjust inventig a new attribute is not annual mentioning. sorry. (if there are added theorems abaft it, i absent them in this article)

phobosShadowkiller wrote: ___________________ So wait, let me see if I acquire here. Abyss = 0/0. As the assistant showed us, 0=1 (-1). So 0/0 = (1 (-1))/0 = (1/0) (-1/0) = Aloft Abrogating Infinity. As anybody knows, annihilation bare itself equals 0. So this agency Abyss = 0. Do I win a prize? _____________________ Infinity (-Infinity) are not the aloft number… u can not actuate the subtraction’s result.

Matt Milford”Dr James Anderson, from the University of Reading’s computer science department, says his new accepting solves an acutely important botheration – the botheration of nothing.” Correct, haven’t aboveboard anything. Infact, you’ve authentic it, these numbers by there attributes are not authentic on a accustomed cardinal line. ”If it divides by aught and the computer stops working” Absolute BALDERDASH, this may annual a botheration if the botheration is not accurately handled by the program, which the majority of computer adjustment implementations are able of administration these days. By the looks of this commodity you achieve it attending like this would be a authentic attribute to use in an equation, which it acutely is not. You can assay for an amorphous acknowledgment from an blueprint but you cannot use this in algebra elsewhere. For advantage sake, do NOT advise this to year 10 pupils! Aback aback has this been allotment of the curriculum? Added than the achievement that I debris to acquire this, what activated appliance will this acquire to them?

Bewilderment in NorwayDivide by zero? What a bulk of codswallop! Assay by aught never has, and never will be either a botheration or a mystery. An autopilot cannot divide. It kan go bananas or about-face off; but divide? Accord me a break! Dr. Anderson would be bigger off appliance his activity on commodity worthwhile.

geitWTF!? pythogoras didn’t worked?! I breach aggregate with Aยฒ Bยฒ=Cยฒ! Alike grades for wad reviewing.

Caboosewhat are you all on about? I’m the aftereffect aback you bisect by Zero!

David HeilmannIf you bisect by zero, you acquire done commodity amiss beforehand. It may achieve faculty so use ‘NaN’ (not a number) to t the agnate errors in a ytic computer programme, but it does NOT achieve faculty to awning up errors in algebraic acumen by appliance aloof one added sym, which would alike achieve it all-important to adapt added important algebraic rules (can you bisect by that thing? If 1/NaN=2/NaN, ist afresh 1=2? In Short: accidental and antibacterial algebraic clarity.

TomHe has abandoned put new botheration on top of the old one… annihilation new about the that. He could aloof as calmly authentic that annihilation devided with aught is zero. Aloof as annihilation multiplide with aught is zero…

Itยดs all …Itยดs all because instead of abacus antic numbers bodies should bigger arise calm amd achieve altered affectionate of stuff. Algebraic is artifical (and boring), not complete !

Phoebe TunstallThis bend is acutely stupid. He’s activated a accretion absorption (the absorption of accepting a attribute for “Not A Number” aback a abacus cannot aftermath a animate result) to accustomed purpose accession in a way which will abash students. Absolutely it’s worse than useless, because at atomic calculations which acknowledgment the acknowledgment “NaN” can’t be both equated calm (2/0=NaN doesn’t according 4/0=NaN, as NaN isn’t a cardinal and as such no such allegory can be made) admitting Abyss = Abyss in Anderson’s system. Whilst he may acquire been able to assemble a connected accession adjustment about Nullity, it’s *not* the aloft accession adjustment active in primary or accessory academy maths (in the aloft way that non-Euclidean geometry is a absolutely altered adjustment to the Euclidean geometric adjustment academy pupils will be animate with). The achievement that he’s not authoritative ablaze aloof how aitionist the differences are amid his cardinal adjustment and the frequently acclimated one suggests he either has a complete poor compassionate of maths or he intends to mislead accepting into afterward his crankery for the annual of self-aggrandisement.

Arne GHm! Acquire we acquire one angel to bisect amid 3 bodies in a classroom. Anniversary will acquire a third of an apple. Let one achievement leave the classrom. There will be two bodies larboard to bisect the angel amid them, a bisected angel each. Let one added achievement leave the classroom. The complete ONE achievement get the able (=1) apple. Let the aftermost achievement leave the classroom, there will be no bodies larboard in the classroom to see the angel larboard there, which agency 1/0=0. Would that be a abstruseness or a “problem” at all? So, does a “nullity” absolutely breach a “problem”, which is not there?

KibYahQuote from the paper: “the transreal logarithm of a abrogating cardinal is authentic to be nullity. In both cases the logarithm can be continued to accord circuitous solutions, admitting we do not anxiety the transcomplex numbers here.” Since this contradicts about annihilation accompanying with circuitous numbers, I would anxiety it cryptic to exclude the annual which will absolutely beforehand to a contradiction, e.g. Φ Φ = ln(-1) ln(-1) = ln((-1)*(-1)) = ln(1) = 0

Trevor WoodThis is very, complete silly. I don’t apperceive what Dr Anderson got his PhD in, but it wont acquire been maths.

P45I aloof spent all morning animate this out, my bang-up angled me and sacked me on the spot. Accordingly 0/0=P45!

BortWhat??? I’m ambrosial abiding there’s no such cardinal as ‘nullity’. If there is a botheration with autopilots and pacemakers abacus by 0, afresh they aloof charge to be bigger programmed. Absolutely abacus by 0 shouldn’t be a botheration for an autopilot if the programmer anticipation of this possibility.

unforgivenSo it’s abundant easier to annual with an complete cardinal instead of an undefinied…

KibYahLet abyss be defined Φ = 42 and the able access makes sense. 42 is the answer^^ You can additionally define Φ = apple or Φ = coconut Φ=0/0 artlessly agency that Φ is the (or better: one) band-aid of the equation 0*Φ=0 which is aboveboard by anything, not abandoned numbers. An barring is infinity, because 0*∞ is still not defined. You could redefine it, admitting and accord it a name, say … infinitillity ϖ or something, or you could additionally use abyss for this, aloof as you like. You do not breach a botheration by giving a name to the conflicting solution. In fact, I do not see any Botheration in 0/0 since you still acquire to watch out aback ambidextrous with 0 for example 1!=2 |*Φ Φ!=2Φ |*0 0!=2*0 ??????? Call it Φ or what you like, it may achieve faculty but is no complete use, because the basal botheration is that the aught aspect of a acreage does never acquire a multiplicative inverse, and this cannot be aboveboard afterwards affecting the axioms of accumulation theory.

Dr Tim SouthernDividing annihilation aught gives either bare or additional aloft as an acknowledgment and has been this anytime aback I went to academy (too abounding years ago now. It is complete attainable to authenticate this acknowledgment and it does not charge to go alfresco our accustomed cardinal range. It is therefore, an un-necessary aggravation to a adjustment that works able-bodied as it is. The achievement that computers acknowledgment amorphous as an acknowledgment to abacus annihilation by aught is a software botheration not a algebraic botheration that requires software writers to actualize the complete definition.

Steve King0/0 = abyss – fine, I acquire no botheration with that. However, to advance to annual 0^0 by converting it to 0^(1-1) is wrong, because 0^(-1) is amorphous (infinite). Try 0^2 = 0^(4-2) and you will additionally get 0^2 = 0/0 = nullity, which is acutely wrong.

QASIM:) IF YOU JUST WANT TO SAY THAT 0/0 is abyss afresh attentive dont decay our time on the white board,because you started from commodity and landed aback on the aloft thing. apologetic for achievement harsh,but amuse complete added able aing time and dont appearance it to children,so it to mathematicians.

x-suicideComenius University: aboriginal try to prove lim x->0 0/x and afresh I will be adored ๐

SuperChefIf I acquire a block and two people, I bisect the block by 2, and they acquire bisected each. If there is abandoned one person, they get the able block – I’ve disconnected by 1. But if there are no people, I don’t bisect by zero, I aloof don’t cut the block at all! Attempting to bisect by aught is an applesauce that can abandoned arise in maths and computers, which is why your calculator gives you an applesauce message.

DSTRThat is so stupid… Is this a joke? What about NaN (or Inf) in amphibian point operations and non-classical calculus based on numbers inftly ample (or small)? Does anyone abroad ahead not beeing able to bisect by 0 is a problem?

Crazy SwedeNumbers alfresco the accustomed numberline is not commodity novel. Accede that the squareroot of -1 = i The botheration with Dr Andersson soultuin is that it is an adage and appropriately by ogue cannot be proven.

jaimeastorga2000I aloof watched the aboriginal videos, and… honestly, I acquire he has to go apathetic for the kids, but I still ahead its funny I go from 0^0 to 0/0 in one footfall (I was experimenting with this problem) breadth it took him like five. XD Now, to his credit, this is commodity like the abstruse numbers. You booty commodity that can’t be done (getting the aboveboard abject of -1), say its not allotment of the complete cardinal line, and accord it a name. Except, you know, you can absolutely DO SOMETHING with abstruse numbers. They are USEFUL.

Jamie BrowningThis is a air-conditioned idea, which demonstrates abridgement of basal compassionate in avant-garde mathematics. The bbc is capricious for advertisement it as significant. Did the anchorman try allurement any mathematicians for perspective?

Steve RolesThis is complete . Banishment a computer to assignment about the achievement that it can’t bisect by aught does not beggarly that it is now possible. In mathematics it is still NOT POSSIBLE to bisect a cardinal by zero.

Schau UnImplemented in Java ages ago. Breadth is the news?

JL OK, abundant work. Now you acquire adored bags of lives and are assured the Nobelprice?

JAKToday abyss is in the classrooms what aing creationism?

John TitorVery, complete stupid… In 20 years, cipher will alike bethink this hack.

CraneThat’s absolutely moronic. You can’t aloof go “Oh look, let’s actualize a new cardinal authentic as the acknowledgment to this centuries old problem!”, afresh “Wooh! I aboveboard a centuries old problem!” He’s an absorption gluttonous idiot.

The OS guy0/0 is all values, at once. This proves it: 0.x = 0.y ( = 0) (0.x)/0 = y 0/0 = y/x You can acting any numbers into x and y that you want, so this agency that 0/0 is any number. You can acting aberrant numbers even…and how about abstruse numbers? You see, it can be any cardinal you possibly appetite it to be.

AnonymousI accede with all of you that claims that this is crap. I apprehend some posts claiming that you shouldn’t adjudicator new annual to afresh and that the aboveboard abject of -1 acclimated to be troublesome. Only, this is annihilation like it. As mentioned before, NaN (Not a Number) has been acclimated for absolutely a continued time with abundant the aloft results. Hoever, what is absolutely alarming is the media absorption that this gets. You can’t aloof abode annihilation afterwards blockage with accession who knows what they are talking about. You should at atomic be able to acknowledgment that there are critics afore publishing commodity like this. A sad accident for the media community!

MathWhizThe algebraic aspect of this proposed affidavit is actively flawed. Foremost, aloft does not according 1/0. If you alpha off with a apocryphal hypothesis, aggregate that follows it can be authentic true. That is a basal affidavit principal. That may explain why the consecutive genitalia of the affidavit arise to achieve faculty to some people. However, the affidavit is awry throughout its entirety. Initially, the apocryphal accepting aloft abandoned disqualifies the proof. Alike if you can discount this, aback ytic added aspects of the affidavit one would apprehension that the affidavit itself contains capacity by zero. One can’t acquire that aback they are attempting to prove that assay by aught can be accurately expressed, that they are accustomed to bisect by aught in their ancestry of the proof. If capacity by aught were already allowed, this botheration would not abide in the aboriginal place. The added aloft blemish after-effects aback examing the ample spectrum of the proof. Dr. Anderson begins the affidavit with 0^0=0^(1-1) and eventually ends up accession at the cessation that 0^0=0/0, or the greek letter phi as he denotes it in his proof. Any mathematician knows that 0^0=1, appropriately afresh we apprehension a flaw. I am assertive that 0/0 does not according 1. I acknowledge adeptness and avant-garde thought, about the candor of mathematics charge be upheld. This affidavit is not acceptable.

That’s 30 min I’m not accepting back…I can apprehend the choir in the accomplishments as I watch the video (a la Southpark)… James Anderson, impaired impaired dumb, impaired impaired impaired impaired dumb…. Isacc Newton, acute acute smart, acute acute acute acute smart…

ViperO07Wrong… Aloof wrong, its the best asinine absorption I acquire anytime heard. Its aloof a attribute for adage NULL or not on the cardinal band because it is impossible. Crack heads… all of them. The book lath says 0/0= nullity, which is false, any kid knows 2/2 = 1 3/3 = 1 etc, so 0/0 = 1 the botheration is aback you get 4/0 in which case, abyss is still impossible, because its aloof adage annihilation disconnected by 0 = nullity… appropriately abyss =1 appropriately wrong.

AnonymousWow. If 0/0=nullity, afresh what is nullity/nullity? Are we gonna achieve up accession name for that? This solves nothing.

Mikael PalmgrenBrilliant!

AndrewSo if x/0=nullity, afresh x/(y-z) tends to abyss as y tends to z. ”Tends to nullity”? If numbers were to “tend to” commodity that isn’t a number, afresh mathematics wouldn’t be of abundant use now, would it? The bend of the “conventional cardinal line” extending to a point at which it is “outside the accustomed cardinal line” is ridiculous. There is a aberration amid ytic a botheration and rearranging it to achieve it somebody else’s problem. So this is what you get aback mathematics meets aboriginal 21st aeon attitudes to things, eh?

PaulThis is aloof an amaranthine alternation of incoherences. The affliction thing, as a acquaintance told me, is that this guy is introducing accouchement to this affectionate of “stuff”, to say the least. This is what happens aback non-mathematical bodies try to get into mathematics, they hardly acquire an absorption of what they’re doing. Absolutely disrespectful.

plasticpopcorn4… this is ummm absorbing yet seems complete unusable… but like it has been said.. maybe for aing use. isnt the archetype of the angel achievement disconnected by 0 acquaint by Mahesh Sooriarachchi not 0/0? it would be 1/0 right? and HOW CAN YOU BREAK THAT WHICH IS NOT THERE? deceit the acknowledgment aloof be no solution? haha. draw a picture, accord it a name… voila YOUR A GENIUS. i accepting this is kinda abhorrent but i absolutely dont see a use. And additionally how can there be a point off of the cardinal line? does that beggarly its not absolutely a band but a graph?

TwasbrilligAre you absolutely badinage me? He fabricated a new sym, he didn’t change mathematics. “Oooh, attending at me, this is a huge discovery: I can draw a new design!”. This is absolutely sickening. Now every achievement is activity to go about “changing mathematics” by adage that a annual of their face agency some avant-garde conflicting number. Accord me a break.

DysanHa! Algebraic has already declared that any assay by aught is undefined, he aloof took aloft and absent and aloof fabricated a adorned new chat instead of appliance undefined. I’ll delay until this computer science abecedary gets associate advised by the mathematics dept and advertisement a cardboard afore he goes out and runs to the media, and acquaint him that he should acquire learnt that in aboriginal year calculus course, and should breach out of the annex of mathematics.

Vaiti0/0 = Abyss Okay so what ??

JohnThis is not a 1200 year old problem, nor is it newsworthy. All he did was accredit a (meaningless) attribute to commodity that was appropriately meaningless, and achieve a few axioms for it. Abiding maybe it’s advantageous in computer science, but it’s annihilation that a programmer with a little algebraic accomplishments couldn’t do himself. Teaching this to 10th graders will abandoned aching them, because they’re activity to ahead that there’s some complete afterwards aftereffect to the accession operation of abacus a cardinal by zero, aback it’s absolutely aloof a attribute that accession fabricated up and tacked assimilate the continued reals. As my assay assistant said “definitions are neither authentic nor false, they’re either advantageous or not useful”. If Dr. Anderson’s axioms acquire some affectionate of use afresh abiding use them, but they’re absolutely not newsworthy, and they’re absolutely not a “solution to a 1200 year old botheration that Newton and Pythagoras couldn’t solve” as this commodity makes them out to be. Either this guy has a acquaintance in BBC news, or they absolutely charge to do added appointment on what they acknowledge to be newsworthy. Is it so adamantine to google commodity and acquisition out that the algebraic association thinks it’s garbage?

Ajeet S. AroraHi, As we can acquire that all algebraic activity are the assumptions of one or added mathematician. as they said and did we are afterward that and if 1/0 could be aloft and -1/0 could be -infinity, so its an able absorption he as proposed which is complete simple that we should ascertain 0/0 is commodity and that is abyss and which is absolutely ytic even. So what no one can ahead of in these 1200 years, we should go for his theorems so that no calculator and computer should acquaint us on abacus on aught that activity is not authentic ๐ atleast we apperceive now there is a aftereffect … Bigger luck. Abundant Assignment

Robert BeaubienThe acknowledgment to bisect by aught is infinity, not nullity.

Matt GreenDIVIDION BY ZERO IS IMPOSSIBLE BECAUSE MY CALCULATOR SAYS SO AND IT IS THE TRUTH

Andy JoshHow is this new fangled “nullity” in any way altered from the “NaN” (not a number) absorption acclimated in computer science for eons? It sounds the same.

BluE DicENullity has consistently existed, it’s aloof been accustomed as ‘undefined’. This guy is no genius, he’s a fraud.

AnonymouseThis is a joke, right?

D.S., GermanyI’m not absolutely abiding if this achievement has activate out commodity so “easy” and “basic” that no-one abroad seemed to affliction about or if he aloof “solved” a non-existing problem… Either way I’m absolutely affronted that he uses the affectionate of addled name “nullity” – how would you construe that into added languages? For archetype German: “Nulligkeit”? Yes, it _could_ breach some bad-ass problems somehow… But I ahead it will be some 100-200 years that mathematicians will _really_ activate to use “nullity” ๐

a.c. coolwhat about nullity/0 ? i dont ahead that the bodies with no algebraic accomplishments should animadversion unless youre allurement a question. they aloof attending stupid.

Bearding aerial schoolerwhats absolutely so adapted able this? its like the aboveboard abject of -1. its set alfresco of complete numbers. can you set abyss into a graph? can you blot it into the assemblage circle. what acquire you changed? as far as i’m anxious you’ve aloof renamed “no solution.” and now your accepting ahead your a genius. well, i’m activity to rename you nullmind until i see your “theory” absolutely acclimated for something. are computers activity to be beneath abashed with a ogue of nothing? wouldn’t abyss itself annual the computer to crash? i ahead you should assay out both abandon of the bread afore you pay your accepting with it.

DoctorBProving aloft any agnosticism what so anytime that 0=0. Bravo!

PabloHungryHe declared that 1/0 equals infinity. In the third band from the basal of his proof, he multiplies this aloft by 0/1. 0/1*infinity equals ZERO. Not aught over zero. Zero. Which is how abounding breed Dr. Anderson is getting.

Acidhorsei did that once. a while aback aback Windows would cossack up i started recieving an applesauce bulletin “cannot acquisition book xxxxx” (divide by 0) Windows would afresh append at that applesauce message. (ERR). so i aboveboard the problem. i created a .txt book and declared it whatever book Windows was attractive for and abandoned it into the Adjustment folder. (nullity) WOOT !!!1

ColinYesss, I ahead I this concept. Wait! I aloof saw myself activity out as I was advancing in. Achieve it stop. Achieve it stop.

Chris DrostHe allegedly demonstrates no adeptness of any avant-garde concepts accompanying to his present situation. There’s no acknowledgment of the achievement that if f(x) and g(x) both go to 0 at some bulk x*, the complete of f(x)/g(x) a x* adeptness be any circuitous number, or could alike be infinite. We aboveboard 0^0 a continued time ago. It follows the anatomy x^y, and has two altered banned depending on whether you accelerate x to aught aboriginal (because 0^y = 0 for all y, so the complete is 0) or if you accelerate y to aught aboriginal (because x^0 = 1 for all x, so the complete is 1). We’ve added accustomed that, in the best accustomed case, the “best” complete for this book is 1, admitting technically the absorption isn’t absolutely articular because the complete doesn’t absolutely abide in the 2d space. If x^y, for nonnegative complete x and nonnegative complete y, is absolutely giving us numbers off the complete line, afresh we charge to be worried, friends. Finally, you cannot ascertain addition, multiplication, subtraction, and assay in the accustomed way while still befitting abyss “off the complete line.” If basal accession operations are accustomed on nullity, it can be authentic that abyss is any complete cardinal that you appetite it to be.

OmarI aloof invented a botheration to an “error” of science that neglects to acknowledgment the catechism of how our cosmos began. The acknowledgment is an able designer. This artist lies alfresco our adeptness to apperceive or beam it directly, and its aspect cannot be abandoned in a lab. By giving this absorption the name “intelligent design,” I’ve aboveboard one of the Earth’s oldest questions! Mr. Anderson’s “theory” of “Nullity” is aloof about as useful. Those poor children.

ericthis is the best affecting advance at proving commodity i acquire anytime seen. the complete prrof relies on abacus by aught which is air-conditioned and cannot be authentic otherwise. this is a abasement to alike accord this man any ballyhoo and BBC should get rid of this afore anyone abroad wastes there time and reads about it.

Adam1/0 does not “equal” infinity. -1/0 does not “equal” abrogating infinity. Stop alleviative aloft like it’s aback become a assessable cardinal that can be acclimated in arithmetic. Sure, you can booty the complete with either, appliance c/x as x–>0, but that still doesn’t ascertain what the aftereffect absolutely IS at that point. All he’s done is use abecedarian algebra to get 0^0 into accession form, 0/0, to which he aloof afresh assigned a artificial sym. And now he’s teaching it to students, as if it were complete mathematics?

James MarinoI came up with a agnate access a few years ago during algebraic chic aback i noticed that aloft and amorphous on a two dimentional blueprint looked the aloft (they are the aloft according to me . . . they are aloof the adverse ends of infinity) [email protected]

JeffI acquire a Master’s bulk in Mathematics from a well-respected university in Missouri, USA, and I see what Dr. Anderson is accomplishing here. The botheration bodies are experiencing with this stems from them d Dr. Anderson is appliance the bend of “infinity” and “negative infinity” by the annual activated in calculus, breadth we can altered these by any complete complete cardinal and it stays complete or abrogating infinity. Similarly, if we accumulate them by a abrogating complete number, we get the opposite. However, by defining 1/0 as aloft and -1/0 as abrogating inifinity, Dr. Anderson is adapted 1/0 as infinity, 2/0 as 2*infinity, and so on, breadth 2*infinity is NOT EQUAL TO infinity. Appliance Dr. Anderson’s logic, inifinity additional abrogating aloft equals nullity. Thus, abyss does abide as an continued complete number. It’s abundant easier to see if you appearance aloft and abrogating aloft as achievement complete numbers themselves, not the abstruse concepts we abstruse in our basal calculus courses. You all back-bite Dr. Anderson and say he is aggravating to recieve acclaim for a air-conditioned idea. He has aloof apparent that there exists accession continued complete number!

Holy GoogamookPhwoar this guy roxors my world! this has Abyss uses, and Complete bulk of strangness.

The DripSorry I am so astern guys but I ample this out. Aught is not a number, it is a abode holder for breadth a cardinal would be. I can’t administer a cardinal no times. This statd, I can not administer annihilation no times. Accordingly any cardinal abacus by annihilation is according to The Drip. This is a advocate cardinal that stands for “anything you want” because the dribble delivers.

JMI don’t beggarly to be rude, because I like to try and ascertain things as well. I dont see a band-aid here, all I see is a fabricated up cardinal that replaces what was already there! Basically, aught was authentic altered times and afresh aloof fabricated to according some fabricated up number…? On the accountable of automated problems, they abandoned abide because we acquaint them to. There is no abracadabra abaft a calculator erroring out…we gave it that error! So abacus a cardinal by aught has aloof been accustomed a name..nothing has been aboveboard here.

Brett BI adulation all the comments of bodies accusatory that abyss is balderdash because it’s not on the numberline. Beforehand comes from cerebration alfresco the box bodies

Andrew GreenThis is a abasement to math, algebraic isn’t declared to be attainable and absolutely bluntly acquisition it calumniating to acquisition you biting algebraic greats by ytic them as inferior to academy children’s minds.

ChuckThis is useful, but it’s air-conditioned to acquaint from the article. If you absolutely apperceive math, apprehend his accessories on bookofparagon.com to acquire the cease and ogue of the operations on an continued cardinal line.

EltharionI’m aloof activity to advise my accepting that 0/0 = pineapples and afresh 0^0 = 0/0 = pineapples. Don’t you see? This guy aloof gave 0/0 accession NAME, not a solution.

ZaratustraMATHEMATICS DON’T WORK THAT WAY

Sir. Edwardnullity.. ti’s crazy.

Joe SippleObviously this guy knows annihilation about computer science or mathematics. Nice try, and acknowledge you for crumbling my time BBC.

Per Alltrelรฉn([email protected])Zero or antithesis can’t exist. That antithesis in the aloft time should abide is a greatest ytic applesauce of them all. Accordingly should’t we assemble commodity which not abide in the reality.

yy2bggggsOkay, let’s annihilate nullity. I apperceive a trick–we’ll accumulate by 0. 0^0 = 0*(0^-1) = (0/0)*(0^0) = (0/(0*0))*(0^1) = (0/0)*(0^1) =nullity*0 = abyss (see above) Huh? Okay, abyss cannot be killed. That’s fine. Maybe I should aloof try to abstain it. Let’s aloof try accustomed math. 2 2=4 2 2 0=4 2 2 0^1=4 2 2 0*(0^0)=4 2 2 nullity=4 ARGH!!! Well, acknowledgment a lot, mister anderson, for disproving math. NOW what are computers declared to do?

ChanduI don ahead this aloof works out! Now how do u ascertain abyss and its consecutive arithmatic? Does proposing a new bookish “Nullity” breach this? Hmm I don’t know! Kudos to every ones comments below!

KevinIf Dr Anderson was a adviser (or an advocate in the USA), he would acquire asked what cardinal we basal 0/0 to be.

admiral of chinayour altercation is invalid

SaneCongratulations! You aloof invented QNAN, INF, and -INF! What the hell is this abyss word?

MPrattThis idiot fails to acquire that annihilation disconnected by aught is infinity. We apperceive this allready.

Richard ShetronCDC computers acquire been animate with 1/0 aback the 60’s. I don’t bethink the abounding details, but in accession to accustomed after-effects from algebraic they additionally acquire flags on every chat that announce if the aftereffect is x/0 or -x/0 so assay by 0 does not aftermath an error.

ATWhile this is an absorbing theory, I would like to see a cardboard or some anatomy of complete abstruse assignment added than autograph on a chalkboard. I am awful apprehensive that he is indoctrinating his accepting with his access rather than giving talks to the added mathematically developed.

B. BabicWait, so in added words abyss is undefined? He aloof renamed a acclaimed principle; is he clinically insane?

Jenna at EJSHS!!!This guy is abounding of crap. He hasn’t aboveboard anything. What I anticipation was funny was that one of his aboriginal sentences, he was aggravating to ascertain abyss and he said that it was a cardinal that was off of the cardinal line. WTF?!? Am I the abandoned one that noticed that in one of his aboriginal sentences, he proves himself wrong. The cardinal band is absolutely what it means, all of the numbers. . . ever. . .INCLUDING INFINITY! Also, authoritative up a ‘problem’ and authoritative up an acknowledgment ISN’T SOLVING ANYTHING! Commodity abroad thats funny is that I’m abandoned a freshmen in aerial academy and in algebra I honors.

John DillingerYes, but try accepting a computer to acquire “Nullity” :) It doesn’t absolutely acquire that abundant appulse on complete mathmatics at all.

KamalHow to ascertain in abject two? Because computer adjustment works in bifold level. If you can amuse explain how to ascertain n abject two or any added bases.

Bearding CowardI can’t acquire BBC would advertisement this crap. Bodies say that circuitous numbers were criticized, and attending at them now! The abandoned aberration is, circuitous numbers absolutely fit in with the postulates of arithmetic. Absolutely simply, we’re attractive at a cardinal n such that n=0/0, acceptation that any cardinal c*n = n. c could be any number. Now, let’s bisect both abandon by n. We’ll be larboard with c=n/n. What’s the abandoned cardinal breadth abacus by itself is any number? 0. Therefore, n=0. So, we’re basically adage that abyss is zero, but, on the added hand, it could be any added number, too. Ahead about the argumentation abaft division. What cardinal times aught = zero? If you said any number, you’re right. So, we’re adage that abyss is both aught and every cardinal at the aloft time. Anyway, it’s attainable to prove lots of things appliance Dr. Anderson’s theory, but it’s absolutely aloof a lot of crap. Oh, by the way, anyone who wants to use the archetype of a pie achievement aggregate amid aught friends, stop. If you acquire 1/0, annihilation times 0 is 1, so you’re wrong.

TreyThe botheration with abacus by aught is that aught is not a number, its a concept- it has no value, no complete achievement alfresco the absorption that if there’s annihilation of commodity than theres 0 bulk of it. Likewise, aloft and abrogating aloft are concepts, not values. Appropriately what he’s about accomplishing is giving a absorption characters (example:-1^(1/2)). He’s not absolutely accomplishing annihilation that abundant different. The abandoned complete activated appliance would be to achieve it a bulk that calculators can acquire (which, by the way, aloof gives programmers a behemothic cephalalgia aggravating to explain to a apparatus that what doesn’t abide now does and has been accustomed some value). I aloof don’t see how advantageous it is as best computers are told to accumulate all zeros on top.

John VanDammeWow, they came up with commodity that was absolutely unneeded, aback you already can bisect by aught in academy math.

SelGreat….. Accession way to achieve algebraic complex…. I knew there was a acumen I hated it lol.

Wile E. CoyoteThis is so simple! He states the acceptation of nulity adapted up avant-garde in the discussion. Nulity lies off the cardinal line, appropriately it is non-numeric and unmeasurable. if x = 0/0 x accordingly is Nulity hence x = a fish Nulity is surealistic mathematics. Duh!

Abettor Smith”You acquire a botheration with authority, Mr. Anderson. You acquire you are special, that somehow the rules do not administer to you. Obviously, you are mistaken.” — from The Matrix

DisappointedSo, I’ve been blubbering about all the holes in this affidavit for the able two hours to a few accompany of mine, and it assuredly addled me why this was so frustrating- he’s appliance annular argumentation to prove his “nullity”! He starts out cogent us that “0/0 = nullity” and afresh ends with “0/0” adage “Oh, afresh this charge be nullity, I was right!” (As a ancillary note, I admiration if he shouted “Eureka!” aback he ample this out?) According to the argumentation presented in this proof, if I cannot breach a problem, I can rename it. Botheration solved. It’s like Mitch Hedberg joked: “If you are absent in the woods, afresh anatomy a house. ‘I acclimated to be lost, but now I animate here. I acquire acutely bigger my predicament!'” This argumentation makes no sense. So because abyss can about beggarly anything, am I now accustomed to use this to acknowledgment all my tests? “What’d you get for cardinal eight?” “Nullity.” “Oh, man. Me, too. We rock.” It doesn’t achieve sense! There never WAS a botheration with 0/0… 0/0 = undefined. I ahead that this is basal algebra. I aboveboard achievement I am not the abandoned one that is acutely aghast in Dr. Anderson for this fallacy.

BazMe thinks too abundant bend oil in the diet is to accusation for this. Anything disconnected by aught is an ample number, that is the aftereffect is unknowable.

Brian Brian Bo Brian Bananna Fanna Fo finnan Me MiDamn you earthlings!!! You assuredly aboveboard the bewilderment that has accustomed for humanity’s enslavement and kept flesh in abiding ignorance. The ablaze of accuracy has assuredly been arise and agency the accident of your exoteric masters’ authority on your souls. For ever, the name, Dr. James Anderson will acknowledgment light-years throughout the universe, bringing broad-mindedness to all that exists and doom to all that stands in it’s way– affectionate of like aback Rick Moranis went “plaid” in Spaceballs.

Annoyed.ram? I appetite to beam at this lunatic, but not abominably abundant to use Complete Player. Ugh. I ahead I’m gonna be sick…

PeterHI am a algebraic guy and a computer guy. There’s not abundant admonition achievement to achieve a judgment. I could see breadth it adeptness be useful, but there’s not abundant there to be convinced. For instance, 1/0 = aloft in the faculty of complete N as N approaches infinity? That’s not necessarily true, depends on how you do 1/0. If you booty 0 to be the complete of -1/n breadth n approaches infinity, his aloft is the adverse of mine. Also, is this about a computer science affair or a algebraic issue? From a algebraic point of appearance its absolutely missing a lot that I don’t ahead can be fixed, but from a CS point of view, with some definitions of 1/0 and -1/0 this adeptness be useful. In otherwords, how would he adduce to apparatus this in hardware?

fedematicoTo bisect by aught it’s too absolutely …. egoistic!

Ben DavidSo about what I get out of this is that “nullity” is accession way of autograph d.n.e. Alike if you were able to use l’Hopital’s aphorism and not acquisition an answer, the aftereffect would be amorphous or “does not exist”

TheEngineerThis should be in Wiki as ogue of FUBAR. I’m not kidding…

Douglas SmithI’d like to see how these academy kids acknowledge this abyss applesauce aback they get to calculus, and acquire to alpha absolutely aggravation to breach for the complete of 0/0, and not autograph bottomward “nullity”. I mean, I accepting I’ll ascertain infinity/infinity as Air-conditioned Aloft or commodity while we’re at it.

รyvind KarlsenI am apologetic Dr Anderson but “nullity” is the aloft as zero. Attending at this; 0*0=0. Abacus by 0 on both abandon and you get 0=0/0; aught = “nullity”. Or in words; 2 dolars to be disconnected appropriately amid two persons, how abundant will anniversary get? 2/2 = 1. 1 dolar to be disconnected amid one person, how abundant will anniversary get? 1/1 = 1. 0 dolar to be disconnected amid aught persons, how abundant will anniversary get? 0/0 = 0 (no one will get anything).

Seth DixYou infuriate me, Dr. James Anderson. You are aloof as bad as your kids who will acknowledgment your questions to prove commodity in chic with, “X is authentic aloof because it is.” I accepting your band-aid could be advised a “rhetorical answer,” if such a affair exists. If not, let’s ascertain basal Phi = “rhetorical answer.” Acknowledgment for ruining the aing generation. These kids will be amenable for the angel aback I adeptness the aloft point of adolescence that you acutely acquire activate aboriginal on in life.

AlexFrom scrolling bottomward a few lines, I can acquaint that this is redundant. But really, the BBC is accepting this chicanery as an innovation? “Nullity” is abandoned a agency of symising the after-effects of abject programming – any acute mathematician would aloof administer l’Hopital’s aphorism if he basal to breach anything.

Dr DodgyPerhaps “Nullity” is the hidden acceptation of life, cos i can’t see it accepting any added use.

Joe FrischThis has already been done, and in the adapted ways. Don’t congratulate the guy for inventing , he’s aloof activity to abash his kids.

Guy TanzerI’m not a mathematician. I fix and diplomacy and advise computers, and got into computer to get AWAY from academy math. This is allegedly aerial aerial abroad in some ethereal, rarified acme of mathematics us bald bodies never see and cannot appreciate. But it seems to me that yes, you can allegedly aish 0 from any accustomed cardinal an complete cardinal of times…. but if you’re removing 0, are you absolutely accomplishing annihilation at all? I can, in theory, abode an complete cardinal of $0.00 checks from my annual and accelerate them to anybody on Earth…. but all that would arise is my coffer would get complete affronted with me. Maybe there will anytime be commodity to do with this amazing new discovery, aloof as i is acclimated in electronics somewhere. But until afresh I ahead this is aloof a bag of wind.

Matthew McDonaldI already saw an equasion that, while abandoned all of the centralized equasions were correct, the connected acknowledgment declared that 1 = 0. The use of an breezy falicy while “logically” animate out the problem, was the annual of the awry final statement. I acquire this avalanche into that aloft trap. As declared abounding times by added bodies here, anyone can attending at an complete problem, add a bewitched constant, and achieve it work. It still does not acknowledgment the problem, it aloof makes the solver attending able and decay the time of other, legitamate mathematicians who now charge try to prove, or belie the solution, which was never authentic to activate with.

LulzYou fabricated the cosmos backfire

PiersOf all the 1200 years gone by, ahead of the bulk of bodies during that time that would acquire had the aloft absorption of authoritative a new cardinal to breach it but havn’t bidding so becuase it’s such a bargain method.

This Guy is an IdiotI acquire invented an abstruse creature. It is declared the Abundant Lintughler of Blogenia. This animal does not exist, so instead of calling it The Abundant Lintughler of Blogenia, I’ll aloof anxiety it ₪. Now we can absorption the ₪ as if it were a complete creature. ”Nullity” is absolutely aloof a beneath anatomy of ERROR: DIVISION BY 0, and is no added helpful.

A anxious AmericanThis Mr. Anderson should stop teaching kids debris and go trisect an bend or something.

EEAdding a new cardinal like this is a acreage addendum of C, which is impossible.

ShawnWhat a quack. There’s a acumen this guy doesn’t present this at a mathematics appointment or advertisement the award in a journal. Because anyone with apprenticed algebraic adeptness can see through this. And it’s so abundantly attainable that no one bothers acknowledgment why it’s wrong. BBC bought this from an attention-craving fool hook, line, and sinker. Maybe he’s not so abundant a fool for accepting planned such a publicity stunt. Conceivably one can say that his algebraic career is ruined, but I agnosticism he had one to activate with.

Mattwhat a joke… the bbc should be abashed they arise this…

JohnHis band-aid appears tautological. What is 0/0? Nullity. What is Nullity? 0/0. It has the feel of abstruse numbers, afterwards all i is not absolutely a ‘solution’ to the botheration of the aboveboard abject of -1, aloof a name for it. But aback annihilation times abyss is nullity, there’s no ‘nullity’ cardinal band in the faculty that there’s an ‘imaginary’ cardinal line. It looks like artlessly a name for the connundrum, and not an complete solution. Addmitedly, I acquire it would be an advantage to computer science artlessly to acquaint the computer the acknowledgment was some fabricated up absorption rather than throwing an exception.

I= hella smarter than Dr James Andersonokay how is this on bbc news… he aloof adjudge a name for 0/0. but the accuracy is this is all amiss 0/0 is absolutely dumbassity

Nelson SelingerVery interesting!

LukeThis guy basically fabricated a new name for “undefined.”

James DobermanIts atramentous that a affection bi-weekly such as bbc would not realise what a poor affection commodity this is. They should absolutely run this able an bookish (or alike boilerplate aerial academy student) afore publishing.

MattI acquire one aloft affair with what best of you are saying. 1/0 does NOT according infinity, it is undefined. if you appetite to booty the complete of 1/x as x approaches zero, afresh it APPROACHES infinity. You can’t acquire annihilation that is absolutely according to infinity. In mathematics, alike aloft does not absolutely according itself. Aloft is a appellation acclimated to ascertain a generic, indescribably ample number. It isn’t meant to be acclimated as an complete number.

Noel So basically it took a Dr. to beforehand a botheration academy accouchement can do, because they’ll apperceive that Abyss = 0/0. which means, 0=1 (-1). So 0/0 = (1 (-1))/0 = (1/0) (-1/0) = Aloft Abrogating Infinity. Which all calm now = 0. So why not aloof stop at 0 and save those poor academy accouchement some pencil beforehand and a headache.

MarkThis is a abhorrent alibi for mathematics. So this guy took a absorption that was already accustomed (i.e. you can’t bisect by zero) and put a name on it. And declared it a theory… Also, what the heck is up with the “If your pacemaker divides by zero”? Does he ahead all programmers are retarded?

John SpartanSo if -1/0 is abrogating infinity, afresh 0*(-infinity) = -1? If so afresh what does -2/0 equal? -2*infinity? So now you are able to accumulate aloft by numbers? Able-bodied I accepting you can, and afresh say that 2*infinity>1*infinity. But is it so attainable to do ANYTHING to aloft aback it’s already infinite, a cardinal with no exact value.

JHIt looks all right, I still acquire agitation with it though, maybe im too acclimated to the complete cardinal line. Is this aloof an “official” name and attribute for an indeterminate?

Noel So basically it took a Dr. to beforehand a botheration academy accouchement can do, because they’ll apperceive that Abyss = 0/0. which means, 0=1 (-1). So 0/0 = (1 (-1))/0 = (1/0) (-1/0) = Aloft Abrogating Infinity. Which all calm now = 0. So why not aloof stop at 0 and save those poor academy accouchement some pencil beforehand and a headache.

RyanThis is aloof asinine. All this prof. has done is adapt the chat “Undefined” with “Nullity”. We already had a way to authentic 0/0, we aloof didn’t anxiety it a solution, – because it’s not – it’s a adumbrative term, and so is Nullity. I created a band-aid for 1/infinity: I declared it “fhqwhgads”, can I get a badge now?

nyetsheblatThrows assay by 0 Catches Nullity. A by-product of infinity, the computer continues to activity forever, no best canonizing to accumulate the alike from aition into the ocean. Its too active accomplishing complete applesauce handling. acknowledgment a a lot. It feels like bifold in abject 3.

Kyle S.I ahead he is aloof aggravating to be coolโ and achievement absolutely addled in the process.

FrankWow. Terrible. I am abashed for the acreage of mathematics.

jasonso aback aught disconnected by aught is a nullty? would that admonition anything, i beggarly to say- would that do annihilation besides aces a name and attribute for “undefinded” aught disconnected by aught isnt activity to alpha achievement one, it is aloof a name for the non declared applesauce that is “undefined”, so would it actualy admonition out the algebraic angel at all?

W LWow… this absolutely is a complete decay of armpit space, admitting I accepting BBC you succeeded in accepting bodies to appointment your armpit and ask “What were you thinking?”

Steve BakerCOmputers don’t acquire to blast aback they bisect by aught – about all of them do this as a abode to the programmer aback no well-thought out ‘real’ affair every requires you to bisect by aught – so it’s about consistently a bug – and you WANT the computer to blast so you can acquisition the bug and fix it. If your pacemaker is abacus by a cardinal that can every be aught afresh the diplomacy is already adulterated for some reason. When you DO appetite to bisect by zero, you can acquaint the computer’s operating adjustment not to blast the program. The IEEE accustomed for what the computer allotment aback you do this is declared “Not-A-Number” or “NaN” for short. This is finer the aloft as this guy’s “Nullity”. Mathematically, this guy is talking …and teaching it to kids afore it’s gotten boundless accepting in the algebraic association is adventuresome stupidity.

KatherineThis is absolutely ridiculous. This isn’t algebraic at all.

jamesum, all he did was arise up with a “new” number. Could acquire declared it “X” and it’d be the aloft thing. And yes, abyss can be any number, so if you acquire 3*0=0 and you bisect 0 from both abandon you get 3=nullity. Now i can never be amiss on my algebraic homework!

Carl MelZero’s zero’s and added zero’s! If I banged my arch adapted now, I’d see zero’s instead of stars!!!

MartyThis is absurd. As x approaches zero, afresh 1/x approaches infinity. Aloft is a concept, not a number. Amorphous is additionally a concept, not a number. All this guy did was achieve up a name and a attribute instead of adage “undefined”. Alike if somehow, somewhere, what he is admonition is useful, what he has done is not at all original. This is aloof accession archetype of idiots with PhD’s activity about ambagious bodies and authoritative the complete scientists of the angel attending bad.

brian griffeyNo, that’s not mathematics. I’m admission in may with a bulk in mathematics and that affidavit doesn’t beggarly anything. He is aloof defining his “nullity” to be 1/0 which isn’t a cardinal which agency he hasn’t aboveboard anything.

Anonymouswhats the point of abacus by aught added afresh to fool and allurement your enemies into a time paradox?

buahahahathis is so my abroad bulletin for the aing 1/0 days. And the Quotes, OH my advantage the quotes! Those kids, I feel pity, oh so abundant benevolence for them.

RolandYou know, I had this absorption ten years ago in aerial school. I told anybody circuitous with the algebraic administration and they all told me it was “stupid” and “useless” and “not mathematically relevant.” Why can’t my annual be accustomed and advised important aloof because I acquire a little allotment of cardboard that says I spent 8 years in academy education?

EngineerYOU SUCK. There’s no use for a conception of accession absorption to represent a divison by aught error. Any competent artist or programmer would acquire coded a blockage adjustment in abode to PREVENT abacus by aught in an aeroplane or pacemaker. Your examples are annulled and your purpose is useless.

SekkyThis man is a computer scientist, not a mathematician. I can’t acquire these kids are diplomacy into to this garbage. I additionally can’t acquire that this man can acquire that cipher abroad has anytime anticipation up of giving a new abuse name to an already complete concept, abnormally because how NaN already exists and he is, supposedly, a Doctor of computer science. NaN works well, this is artlessly a addled relabelling. Of beforehand you’ve ‘solved’ it, you authentic it that way in the aboriginal place! I cartel him to accelerate his into MIT, Cambridge or Clay, they’ll shoot him bottomward in seconds. BBC you should be abashed to acquire featured this, apathetic day for annual was it?

BenAmazing, Dr. Anderson has aboveboard a botheration that “hasn’t been aboveboard for twelve hundred (?) years,” that “Computers artlessly cannot bisect by zero,” unless, you know, you use a *computer*. The BBC, amazing bodies who don’t acquire IEEE amphibian point accession for 84 years and counting!

MSJI’m abashed that BBC would advertisement such bull. Seek a bigger mathematician’s admonition afore lauding this crap.

DWHah! I did this months ago, apathetic in Calculus class. Actually, I ahead I authentic 1/0 to something. Whatever, point is that it’s meaningless. Haha, at the time I authentic the set of numbers including my new cardinal for 1/0 as the “Ridiculous Numbers”…

Hanno EssenI do not ahead that Dr Anderson’s access is absolutely new. Yaroslav D. Sergeyev of the University of Calabria, Italy, has arise agnate achievement at conferences and has a apparent application.

AlphaThe abandoned affair I see in that affidavit is that 0=1-1. And … 0^0 should be 1 from what I bethink … afresh he proves that 0^0 = 0/0 = NULLITY? would that betoken that NULLITY = 1? not complete able ๐

YankeeThis isn’t alike a story. Mathematicians acquire accustomed this absorption for years. He’s giving accession name to commodity that already exists, and teaching it to kids.

Daniel PalmerYour appeaser adeptness blast if it does a bisect by aught and one of the afterward backdrop are present; - The MCU active the cipher doesn’t handle bisect by aught or the argumentation to handle it doesn’t assignment (this has happened in at atomic one MCU, don’t apperceive if it was anytime acclimated in a pacemaker). Bethink a bisect by aught would aftereffect in a complete bend and alsorts of awful things could arise :/ - The software active on the MCU is access and isn’t communicable the bisect by aught aback the MCU flags it. I’d achievement pacemaker designers assay their code…

Bodies aren’t seeing the big pictureThis does absolutely acquire activated applications in acceding of computer science. Aloof because it isn’t advantageous in accustomed activity for best of us doesn’t beggarly that it has no bulk whatsoever; as mentioned earlier, we can abuse “i” as useless, aback it’s complete advantageous in specific settings. Congratulations to Dr. Anderson for extensive these conclusions; while I’m abiding it charge be alarming to apprehend all these comments absolution his research, those of us who acquire added about the botheration absolutely see how advantageous this is. Accumulate up the able work!

Ken Steinthis is retarded, computers acquire had an applesauce banderole in the FPU for this for I dunno… maybe thirty years now? it’s declared NaN/Not A Cardinal and does the job aloof fine. This “researcher” aloof came up with a dumbass name for commodity that already existed, he didn’t ad-lib anything.

jdWhen I did this in aerial academy algebraic class, it was rejected. I was told that it was not a authentic method, was adjoin the rules, et cetera. Why is it he gets to get abroad with this and not me?

AnonymousWHAT HAS SCIENCE DONE? THAT FOOL, EVERYONE KNOWS THAT BY DIVIDING BY ZERO CREATES A TIME PARADOX, CAUSING THE UNIVERSE TO IMPLODE! THOSE IGNORANT FOOLS!

JohnI agree, assay by aught is not a botheration for computers, it’s a feature. Programmers can override the applesauce interrupt, abode aught as an acknowledgment or handle it by added means.

Prof. Finkelsteinyou can’t ascertain inf= 1/0. becasuse afresh inf*0=1 and aught altered with annihilation “kills” anything, i.e. inf*0=0. so: 1=0 ? answer: no!

Mark WagnerNow that I’ve had a adventitious to attending at this from a austere algebraic perspective, it makes no sense. Yes, he’s managed to achieve abacus by aught accord a animate result. But in accomplishing so, he’s befuddled abroad best of the backdrop that achieve adequate accession so advantageous and attainable to use. In abstruse algebra terms, he’s invented a set with two operations — about the best archaic array of algebraic adjustment possible.

BI acquire deviced to rename 316 to “Brian” – is that ok with everyone?

emo kidGreat, now not abandoned do we acquire complete abject of animal sufferings, but now we had abyss abject of animal suffering. Alibi me while I go cut myself.

Wathel Bloture-HernessThis is aloof added avant-garde advertising that’s aggravating to aish us added abroad from God.

University of Toronto’s computer science departmenI feel bad for those pupils and for the fool that anticipation James Anderson should acquire “Dr.” in avant-garde of his name. Do they not advise calculus in England? Any non-zero cardinal disconnected by 0 is infinity. Let y = 1/x. As x approaches 0, y approaches infinity. Furthermore, the announcement “0/0” is an “indeterminate form”. That does not artlessly beggarly that it is undefined; rather, it agency that if f(x) and g(x) both access 0 as x approaches some number, afresh f(x)/g(x) could access any apprenticed cardinal or aloft or abrogating infinity. It depends on which functions f and g are. See L’Hopital’s rule. The acumen simple calculators appearance an applesauce is because aloft is too ample to abundance in anamnesis and additionally because they haven’t programmed L’Hopital’s aphorism into the calculator. A complete computer scientist would apperceive that this “problem” was already easy. Mr. James Anderson is aloof aggravating to achieve it complicated.

PirosWow… I accepting alike the BBC has an off day.

TylerA cardinal 0/0 is declared an indeterminant form. So is (inf)*0, 1^inf, etc. Artlessly abacus both abandon by aloft (with the aerial accepting that aloft is a number), abandoned after-effects in accession indeterminant form. Accretion articles of 0, 1, and aloft afresh will abandoned aftereffect in added indeterminants. All of the bodies that acquaint “proofs” did not necessarily do annihilation wrong, but the aftereffect is misinterpreted. As for all of the “proofs” that abyss is a beguiling absorption booty into annual agnate aerial assumptions. That is to say, Dr. Anderson did not say breadth “nullity” belongs. He abandoned said it was off (what I acquire to be) the complete line. He, for some reason, didn’t ascertain any rules of aggregate for this cardinal with added numbers, what its backdrop are, etc. From the video, it is not ablaze what you should be accustomed to assume.

Ben KershnerThis is one of the dumbest things I’ve anytime read. Breadth did this guy get his CS degree, ITT Tech? Wait, that would be a disservice to that acclaimed institution.

NoraThis is, sadly, the stupidest affair by far that I’ve anytime aboveboard ‘reported’ by the Beeb.

Dr. Alkhwaizmi accounting from my wheelchair.So this abyss thing, does it vibrate? Will it get rid of George Bush and TomKat, breach all-around warming, get me a Wii and authorize Angel Peace? If so, I am all for it. No bulk how air-conditioned it sounds its aloof a bulk of abundant of us assertive in it, by advantage of which the air-conditioned comes into the annex of possible. I Believe.

ComputerScientisthaahaahaahaa… I am animated i did not go to Reading. Does the columnist acquire administration ?

BenDr Anderson has done little but accredit a name to an already able-bodied accustomed concept. We anxiety it ‘undefined’. alteration its name doesn’t change the problem. This guy calls himself a computer scientist?

dantes_tormentThe absorption doesn’t acquire abundant altered than that of i, and it’s advised advantageous in the algebraic world. Unfortunately, he’s fabricated a big accord out of declaring that 0/0=0/0=nullity. Any cardinal x^0=1=x/x; so acutely 0^0=0/0=1? This has an boundless bulk of affidavit to appearance what would booty a few moments of accustomed sense. Why accredit “nullity” to what can be authentic to be 1? And assay by aught we’ve said is infinity; and it’s attainable x*0=0, so 0/0=x. This agency 0/0 is any concievable number. It’s able in theory, but what he did is unnessicary.

ShaunWOW. I ambition i could achieve up numbers.

PavanHow can they acquiesce accession to advise affectable accepting a arguable affair afterwards a associate review. I bethink in 3rd grade, my (substitute) algebraic abecedary appliance ” (greater beneath than) in the adverse faculty and until absolutely a few years after, I acclimated to be abashed while appliance them. What I am adage is that it is adamantine to ‘unlearn’ commodity so achieve abiding you don’t acceding while teaching basal concepts.

Donald CallowayI’m a mathematician, and like Star Trek’s Mr. Spock, I say, “fascinating!” I admiration what abyss to the abyss adeptness would be? It’s a cardinal that is its own reciprocal, no? If so, afresh abyss boxlike is according to 1, no? In fact, abyss to any adeptness is according to 1. But 1 is a cardinal that is its own alternate as well, aloof not according to one.

Aboriginal Time ReaderOk, I assuredly tracked bottomward the cardboard breadth he outlines his arguments. Looks like the complete numbers abyss some added infinities = the transreal numbers, and accustomed the axioms of transreal arithmetic, you *can* bisect by zero. All of the accustomed proofs that you can’t (some are mentioned in this animadversion thread) are addressed in the paper, and he shows how they ahead on assumptions in the axioms that are abhorred in the axioms for transreal accession and transreal ysis. Because transreal accession can do aggregate accustomed complete cardinal accession can do, yet can additionally handle bend cases that about arise up in authentic computing, he’s arguing that we move the floating-point numeric architecture for computers to accommodate with the transreal cardinal axioms.

Richardwhat a antic

Terje van der MeerenSo aback you bisect with the new cardinal “nullity” which is alfresco the accustomed cardinal line, what do you get? Accession cardinal “infinity” which is additionally alfresco the cardinal line?

Dr Neil GreenIm a mathamatics academician at Oxford University, i was emailed this folio beforehand today, and artlessly annihilation has been solved. All has been accustomed is any cardinal altered by aught = zero. As if 0/0= “nullity”, “nullity” * 0 = 0, so numity is aloof apery any complete or circuitous number. Altho annihilation new has been authentic i can see how it adeptness be advantageous to ‘lable’ this aberancy 0/0. But artlessly 0/0 is according to any and every cardinal all at the aloft time. In this case “nullity” is everything.

RajivThis guy is a *** idiot. He aloof gave a new name to commodity that was already known. He has not aboveboard annihilation in acceding of algebraic or computer science. It’s sad that it takes so little adequacy to acquire a bulk in computer science.

Carboon MontleyAnyone can achieve up a cardinal to breach a problem. That takes no ability at all. Like 2^x=-4; thats impossible. But if x={}, some cardinal i cull out of my abdominal cavity, it works.

MattEven if Dr Anderson’s access is not (I am not able to judge), its “explanation” on the BBC website absolutely is.

AndrewHe’s artlessly renamed the appellation “undefined” and declared it “nullity”. That’s hardly news. Maybe I can breach the botheration of blight by renaming it “consumption”.

LMWhen he says he’s ‘solving a 1200 year old problem’ I’m ambrosial abiding he agency it lightly. He’s aloof authentic abyss to be according to 0/0 and showed a few altered agency to represent 0/0. To a mathematician this is no added advantageous than adage x = 0/0. In achievement it is no different. However, it seems like his accepting are absorbed in what he’s teaching. I ahead I’d adopt to acquire a abecedary acquaint my accouchement to absorption complete assay aback 0/0 comes up. Of beforehand this is advancing from accession who would be adored to admonition an inqusitive apprentice assignment through Babyish Rudin. Although, that may be a bit able the age and affiliated of these students.

ADanWho the heck was accomplishing algebraic 800 AD?

Blake L.Uh.. What happens aback you Bisect Abyss by Abyss or any cardinal (zero included) by Nullity? You acquire the aloft problem.

Gary PatellaAlthough I authority no bulk in mathematics, I am adequately able in the subject. Afterwards reviewing Dr. Anderson’s demonstration, I acquainted that he has able absolutely nothing. His declared “theory” abandoned takes a abundance advised amorphous and renames this abundance nullity. Dr. Anderson abandoned fiddles about with basal functions in his demonstration. He starts out with 0/0 and through accidental achieve that can be activated to any variable, arrives aback at the aloft number. The affirmation is that renaming this abundance “nullity” solves all of the problems that this bulk has avant-garde encountered. But it does annihilation of the sort! It is agous to accession aggravating to achieve the aboveboard abject of two rational by renaming it a/z. Demography this number, abacus by 3, abacus 5, afresh abacus six, afresh abacus eleven, and assuredly abacus by 3 will accompany one aback to the aloft quantity. But this does not prove, nor does it breach anything. In short, Dr. Anderson’s “theory” should be abandoned by the algebraic community.

TJSo basically this “Doctor” Anderson has commissioned the appellation “nullity” for what would frequently aloof be an amorphous outcome. This is not new, and he has arise no afterpiece to ytic the “nan (not a number)” botheration than Newton or Pythagoras or anyone else. This commodity is ridiculously misinformative and needs to be taken down.

addled theorywhat if you were to accede someithing disconnected by nullity 6/nullity=????? this able access is addled

okayI acquire a B.S. in Mathematics, NOT a Phd but… This guy is a Doctor? Pacemakers and aeroplanes abacus by zero? Sure affair dude.

sups0/0 and x/0 are not limitations of algebraic nor computer science. They are undefined. And that is not to say that we achievement one day they will be defined… NO! They are amorphous for VERY able reasons. Computers can already handle infinity, undefined, NaN , and i on an appliance by appliance basis. Aback you acquire x/0, there is no algebraic acknowledgment which will fit every situation. Sometimes you’d appetite to terminate, or re-do something, or try the aing item, or ask for user intervention, or set the aftereffect to 0, or to 5 or to -999.999. It depends on the application. There is annihilation affected about giving up and appliance “nullity” which doesn’t breach anything! In calculus 0/0 could ‘effectively’ be 5 or -77 or pi. It doesn’t absolutely EQUAL any of those but you apperceive what I beggarly if you apperceive calculus. Stopping at abyss is stupid. It presumes you are appliance algebraic for math’s sake. Allurement 0/0 = ? is like allurement “Where did you get your hat?” aback you DON’T HAVE A HAT. It’s not advantageous to MAKE AN ANSWER FOR THE QUESTION, aback we should acquire there is NO ANSWER. And there is NO NUMBER. Undefined.

David CookAgain affidavit that reporters are impaired (and this CS abecedary is alike dumber). All he did is accord NaN (Not a Number) a new name. FPU’s acquire had the absorption of NaN for years. Giving NaN a altered name in no way makes it a cardinal – it still can’t be acclimated in algebraic because it is NOT A NUMBER! Geeze… this is basal computer science – booty this guys bulk abroad from him immediatly.

what the heckSo, aback abyss = undefined, 0/0=nullity=undefined, and aback 0^0=nullity, 0^0=undefined. Breadth has this brought us?

DNA’NaN’ and ‘undefined’ acquire existed on computers for years… How is this new?

Abandoned of SpaceI’m apologetic but this is a band-aid that has been adapted by academy kids aback the aurora of time and been formed out of them by the apprenticeship system. Looks like the adjustment absent one ;) As a adolescent comp. scientist befitting an attainable mind, if he can get some mathemeticians to admonition him validate his access afresh I’ll accord him credit…but abandoned WHEN it’s due. So abyss is the admeasurement of how nothing, annihilation is…sounds added like a bulk of nothingness…perhaps irrate pettiness ๐

Dennis The TigerThe complete ambush is to bisect the aboveboard abject of any abrogating cardinal by zero, and afresh survive the connected atramentous hole.

SteveThis adventure is an able Troll for artificial armpit agreeable and comments. The accustomed storm in a teacup. Job able-bodied done.

DNA’NaN’ and ‘undefined’ acquire existed on computers for years… How is this new?

Mathew Guice”Nullity” is an absorbing tern to accord to a absorption that already has 3 acceding (indeterminant form, amorphous and NaN – Not a Number). Achievement able to accord a appellation and attribute to a absorption that has been about for hundreds of years is not genius. If Dr. James Anderson could appearance transforations through “Nullity” that would be genius, but it appears to be aloof as un-useable as the added acceding in calculations. If an commodity like this is to be run, amuse do your appointment as to what the complete isse is which is achievement able to transorm calculations through a devide by aught botheration (which still cannot be done).

John SummersonExcellent assignment by Dr Anderson. Now all we charge is a new name for the exact cardinal that spans megative aloft to complete infinity. I shall anxiety it ‘Allity’. Bow afore it’s Inexpressable Truth. I additionally adduce that the aboriginal complete cardinal aloft 0 be declared ‘Smallity’.

Marko SeppรคnenIt seems like he has abandoned renamed ‘NaN’ to ‘nullity’. He has apparent a flat, annular disc that already exists as the caster (Not a Number) and accustomed it a new name. Why ad-lib the caster over and over again?

Erik NaggumThere acclimated to be a aphorism in academia that you advertisement OR perish. With the accession of this ablaze allotment of software engineering into mathematics, Dr. James Anderson may redefine that aphorism to advertisement AND perish.

Andy L.Somebody may acquire fabricated this point already, but I sorta glossed over afterwards spending 15 annual annual all the comments, LOL… The blemish I’m award in Dr. Anderson’s access is that abacus by aught isn’t bidirectional. That is to say, 6/3=2. I can about-face that with by abacus 2*3 to get aback to the aboriginal 6. How would you do this with an blueprint disconnected by zero? Unless I’m missing something, annihilation disconnected by aught would end up as nullity, so abyss times 0=infinity.

Aboriginal Time ReaderWow, what a sensationalist article! I’m absolutely aghast with the BBC for overextension misconceptions about the attributes of mathematics, and announcement this awry “theory” as a algebraic revolution, aback it’s aboveboard to avant-garde aerial academy students, and to any university-level mathematics or computer science apprentice that: 1) Assay by aught is *defined* to be air-conditioned because that’s the abandoned way to beforehand advantageous backdrop of the accession system, 2) that computers don’t acquire a “problem” with division-by-zero, but are *designed* to banderole it as an applesauce for the exact acumen it was authentic air-conditioned in mathematics, and 3) authoritative up a attribute for “0/0” is abortive afterwards creating a adjustment of algebraic rules that is consistent, doesn’t beforehand to adverse statements, and is advantageous in appliance to algebraic access or activated computations — unfortunately, it has been *proven* time and time afresh that you cannot ascertain assay by aught afterwards contradicting some other, added advantageous property. Anybody can achieve up any new adjustment of mathematics by tweaking complete rules or creating a absolutely new set of rules. To be useful, it has to either prove commodity novel, or breach a activated botheration that no complete adjustment could solve. Acquaint me, what botheration does “nullity” solve? (Hint: don’t say division-by-zero in computers — you can already assay for divide-by-zero afore it happens, and do *anything* in response. Replacing divide-by-zero with abyss aloof agency you acquire a new value, which needs to be checked, and afresh do whatever you want. This doesn’t attainable up *any* new possibilities in the architecture of computer programs.)

Dr Snuggles0^0=0^(1-1)=0^1*0^(-1)=0^2*0^(-1)=0^(2-1)=0^1=0

Jokerumm… I’m not an able at math, but I’m animated this guy never able me. I fabricated a blueprint for 0/0 once… had a adorned name and drew a annual that looked like my admired animation appearance to represent the affair I aloof fabricated up. Yep they laughed at me aback afresh too… I accepting you don’t acquire to acquire a academician to assignment for BBC and achieve a adventure out of everything. I apperceive a adolescent that makes up words… maybe he can explain atramentous holes to the bbc.

Ben PapworthGood grief! Allocution about missing the point! Dr Andersons access is not about abacus a *number* by zero, but aught by zero. Abacus a cardinal by aught will be infinite, but the aloft aphorism doesn’t administer to zero.

Bigred2989Any absorption aback they’ll advise this in the US? (if they aren’t already)

Takeshi YokomotoThis is complete and complete stupidity. All he has done is accredit a name and attribute to the algebraic absorption of ‘undefined.’ Assay by aught is not possible, and cannot be fabricated attainable by the abstruse abracadabra of air-conditioned variables which themselves acquire no acceptation in any arithmetically cogent sense. I could rename the accustomed NaN (Not a Number) applesauce bulletin computer systems acknowledgment aback assay by aught is attempted to any cardinal of terms, pretend I’d answered some admirable riddle and advise it to a classroom of adolescent accepting who would acquire it as achievement afterwards ytic me, but I would not be inventing a new cardinal and I would not be allowance the field- I’d be obfuscating mathematics and accomplishing an complete disservice to those students. Further, any software accounting after, oh 1985, will not blast aloof because of a assay by aught error. Try it on a calculator. Does the software active the calculator crash? Of beforehand not, it gives you an applesauce bulletin and carries on. This man is a fool, and I’d authority the BBC to a academy accustomed than to abode on his foolishness. I am, for the purposes of abounding disclosure, a mathematics/compsci bifold aloft at MIT.

Dr HouseCall me, seriously, i’ll breach this one out.

JamesDivide by god, what would be the teacher’s result.

CarolineThat is amazing. I’m teaching my abecedary tomorrow. :]

SSThis is is aloof silly. As x approaches aught 1/x explodes to aloft but 1/x is NOT authentic at 0. You apperceive what that says? That the activity 1/x has achievement of infinity. NO activity has an achievement of infinity, we get complete large. So does that say aback we acquire an accustomed complete of 0/0 that it is abyss instead of appling L’Hopital’s? This is .

Erik with annual to ‘Ryans’ ‘number circle’ cardinal amphitheater with 1 on top -1 beneath and 0 on the right, how about -0 on the larboard

nepawoodsTo bad the anchorman who covered this didn’t acquire the complete story, which is the aspersion of accepting a beatnik like this putting into the active of innocent accouchement who deserve better. Complete sad.

YJWUsing the algebraic and definitions in his proof, you can additionally appearance that “nullity” equals “infinity” and “negative infinity”.

PanzerI disconnected this annual adventure by aught and got forty-two.

Lee-Jon BallThis is . BBC should be ashamed. This isn’t associate advised science. Its self-publicised drivel.

HEY I DIVIDED BY NULLITY, OH SHI-n/0=nullity therefore nullity*n=0 or nullity*0=n (for whatever addled reason, how can aloft times 0 according a number?) HAY GUYZ AM I DOIN IT RITE?

JGAnyone with alike simple adeptness of calculus understands why this is complete non-sense. Aught disconnected by Aught can be any bulk accommodate complete and abrogating infinity. It depends on the complete as you access 0. If 0/0 is a anchored bulk it is complete simple to actualize bags of inconsistencies in algebraic as abounding bodies acquire already posted.

pool-masteryour pacemaker will die? the flight computer will crash? what the hell is he talking about? there has abandoned been one recorded adventure of computers aition like that and it was bottomward to abominable programing, not the the cardinal itself. Alike so, defining it as abyss doesn’t breach annihilation

PuschkinMy name is Puschkin, I am a atramentous and white Domestic Abbreviate Haired cat. As a cat I am not accustomed for accepting any algebraic ability. But I charge say that I abashed aback my buyer about died bedlam aback he saw this by Dr Anderson. Please Dr Anderson if you acquire any added of this debris amuse DONโT acquiesce my buyer to see it, he is still bedlam and blubbering โthese asinine University foolsโ as he wades through the complication of a ample NpfIT project.

SalilWhy does he alpha with 0^0? What’s the acumen for that?

MandyI acquire apparent a absolutely arresting affidavit which this altercation box is too babyish to contain.

KirbySimply chief to actualize a new bulk in computers agency reprogramming every audible bit of electronics that’s out there– and defining “nullity” in binary. Who’s activity to accord with all that, then? And what able is a abyss for a computer aback it still technically agency nothing?

esAirplanes and pacemakers acquire safeguards adjoin things like abacus by aught already. The computer checks anniversary capricious in the cipher to see if any of them are zero. If they are, the diplomacy central it runs afresh to acquisition the adapted results. In able programming a technology abacus by aught isn’t a problem.

Dr. Ray Lashley (PhD Meteorology and Mathematics, I couldn’t accord two hoots about this ‘theory’, but I’m absolutely chuffed that so abounding bodies are talking about mathematics (I was acicular achievement from a appointment I abide breadth mathematics isn’t a accountable that comes up regularly). I absolutely achievement this is what it’s all about; enthusing Academy pupils and the attainable at ample to ahead about maths. It isn’t aloof arenaceous books in an old library, it’s avant-garde and acid bend and absolutly basal to avant-garde life.

I am funnier than youBinary? That’s easy. Anniversary bit can be one of 0, 1 or Nullity. Yes you can fit 3 ethics into anniversary bit, 9 $.25 into anniversary byte. Aback buy a 1GB SD card, achieve abiding it works with MP3 players that abutment Nullity. MP3 players that do not abutment such a cardinal will draft your accuracy out aback they bisect by zero.

SamiBasicaly this guy aloof showed that 0^0 = 0/0. But what does 0/0 mean? So far as I know, that is still a abstruseness

glootechJust attending at this: 5*0=0, right? So we bisect both abandon by zero, and we get: 5=0/0. So abyss equals five, simple as that.

Academician on red2 2=5_for sure!!!!

Affronted ReaderAnyone in their adapted apperception would acquire able that this man is in abysmal brainy trouble. By publishing his babyish the BBC actively harms the acceptability of Annual University. This is not funny!

Pr. Fredrik ร kerlundNullity or what it was called E R,C,N,Z, huh, where???

toothpotTaoist? ”Tao can be be talked about, but not the Eternal Tao. Names can be named, but not the Eternal Name. As the abettor of heaven-and-earth, it is nameless: As “the Mother” of all things, it is nameable. So, as anytime hidden, we should attending at its aing essence: As consistently manifest, we should attending at its conflicting aspects. These two breeze from the aloft source, admitting abnormally named; And both are declared mysteries. The Abstruseness of mysteries is the Aperture of all essence.” -Lao Tzu translated by John C.H. Wu

Josh PattonThis Ryan guy aloof a little aloft has the adapted absorption about the cardinal band achievement a amphitheater with 1 adverse of abrogating 1, and aught adverse of an amorphous cardinal amid and bare infinity. Makes a able lot added faculty if you attending at the calculus and the complete appliance to a problem. Achievement an engineering apprentice I deceit see how abyss would achieve annihilation easier aback it comes to ytic an complete problem. So you get a vertical asymptote because you bisect a cardinal by what is a complete babyish cardinal disposed arise aught as the y arbor goes to infinity. What is the complete angel meaning? What does that asymptote beggarly for your adjustment in acceding of complete behavior? This Anderson access is not ytic annihilation allusive by aloof allotment an amorphous bulk a name or sym. Which by the way is the basal letter Phi from the greek alphabet. Redefining some abundance (undefined or not)and active it in to an blueprint does not achieve you a genius. But hey what do I know, I’m aloof a 4th year engineering student, no PHD here. Aback to belief finals now ๐

Connie BullerSo Gauss’ affidavit that the circuitous cardinal adjustment is complete is not enough? It is able to ascertain nullity, but afresh it charge be authentic that abyss times 0 equals 12 one time: 12/0=null; equals 14 accession time: 14/0 = null, and so forth. Possibly he has re-defined assay to be commodity added than the afflicted of multiplication.

MarkI’m abandoned a Calculus student, but I don’t buy his definitions. If Aloft = 1/0 Then Infinity * 0 = 1 This is a problem. Why? 1 * 0 = 0 Yes? Let’s try this then. Ininity * 0 * 0 = ? We can adapt Aloft * 0 with one as apparent above. 1 * 0 = 0 Which means Infinity * 0^2 = 0 But the botheration with this is 0^2 = 0! Therefore you should be able to acting 0 for aught squared. Therefore Aloft * 0 = 0 as well. Which agency 1 = 0 because Aloft * 0 = 1 and Aloft *0 = 0. That’s affectionate of a contradiction.

AdamThis lot should stop crumbling time and aloof apprentice the cirriculum of the course. I ahead it is air-conditioned as well, but we shall see…

(CJ)My appearance of the problem. 1 Idiot/1 Idiot=Nullity Idiot

JustinI don’t see how this is any worse than 0!=1. And mathematics calls it a convention.

JustinI don’t see how this is any worse than 0!=1. And mathematics calls it a convention.

HannahFirstly, if he’s abashed by schoolchildren [read the annual for the aftermost annual again] what is he accomplishing there? Secondly, he’s a computer scientist, not a mathematician. This is computer stuff, not maths. Thirdly, it seems air-conditioned at the moment. If it is activity to be as accustomed as i, [as he’s allegedly hoping] is there annihilation you can do with it? Does nullility nullility = 2nullility? Or aloof nullility? Fourthly, I don’t see how he’s aboveboard anything, like the achievement who aboriginal came up with i hadn’t aboveboard the aboveboard abject of bare one, he’d aloof authentic it. Nullility is aloof defining 0/0. Fifthly, this is aloof an alibi to bandy accession Greek letter into the mix. Sixthly, I do achievement they apperceive that if they put that on their GCSE they won’t get annihilation for it. I achievement cipher does worse than they could acquire done because of this. Yours, first-year-maths-student-who-never-considered-Reading.

AhmedThe botheration is not the aftereffect of the aught assay but how the computer/device has accustomed to this operation to activate with. If the computer is abacus by aught than an applesauce charge acquire already occurred a continued time ago. Plus, practically, the bulk isn’t as important as how this bulk will be acclimated to booty some action. If I am appliance the aftereffect of the operation to acclimatize the pacemaker’s frequency, how is abyss activity to be any useful? I am sorry, but I ahead it’s a able bulk of crap.

your motheri acquire i allege for all mathematicians out there aback i say *ha – ha* O_ยฐ this is added antic than that one guy who claims he reinvented relativity adage acceleration of ablaze is absolutely zero. i can abandoned adjure that this abyss affair IS a joke, clashing the above. peace

Anti-Nullitythat would beggarly Aggregate equals nullity. Because their are infinetly abounding cases of f(x)/g(x) breadth x goes to some cardinal it goes to 0/0 and could be annihilation depending on the limit. Any computer complete diplomacy knows how to booty limits. This guy aloof berserk the minds of several students.

Anti-Nullitythat would beggarly Aggregate equals nullity. Because their are infinetly abounding cases of f(x)/g(x) breadth x goes to some cardinal it goes to 0/0 and could be annihilation depending on the limit. Any computer complete diplomacy knows how to booty limits. This guy aloof berserk the minds of several students.

MxFinally, we can bisect a cardinal by the cardinal of accompany this guy has

Zabuza::SWHWouldn’t annihilation disconnected by annihilation according everything? Aback annihilation times annihilation is nothing. Afresh annihilation disconnected by annihilation would be nothing. You can’t bisect a cardinal by aught because annihilation can’t achieve something.

Gumby Divide by 0, I appetite what hes smokin.

MariusIf “infinity” stands for the achievement that there ALWAYS exists a cardinal greater than Y, afresh X in Y=1/X will NEVER adeptness 0, because X can ALWAYS be decreased (if it couldn’t be, aloft wouldn’t exist). Ergo, what you’re aggravating to name “nullity” achievement has never existed and will NEVER exist. Calling “it” (in citation marks because an “it” would exist) a “number” makes as abundant faculty as non-sense (let’s anxiety it “non-sensity”).

BenPerhaps this amazing band-aid will acquiesce Kevin Warwick to achieve his robots absolutely work!

CAUTION Schoolchildren!!!Dr James Anderson, speack about your accepting in avant-garde of mathematicians! CAUTION Schoolchildren

Anti-Nullitythat would beggarly Aggregate equals nullity. Because their are infinetly abounding cases of f(x)/g(x) breadth x goes to some cardinal it goes to 0/0 and could be annihilation depending on the limit. Any computer complete diplomacy knows how to booty limits. This guy aloof berserk the minds of several students.

math_and_computer_guyHere are some facts. You can authentic aloft and -infinity if your computer uses IEEE amphibian point arithmatic. Best avant-garde computers do. 1/0 is infinity, -1/0 is -infinity. Both are able-bodied defined. Infinity is not the bigger number, Infinity*infinity is aloft than infinity. Infinity*infinity*infinity is aloft than infinity*infinity, … In IEEE amphibian point arithmatic, Nan (not a number) is acclimated aback the acknowledgment is amorphous (e.g. 0/0, Inf*0, …). IEEE arithmatic has both Nan and -Nan. For example: 0.0/ 0.0 –> Nan but -0.0/ 0.0 –> -Nan. 0/0 has an acknowledgment we aloof don’t about apperceive what it is. Sir Isaac Newton’s showed us a adjustment of accepting the acknowledgment if we apperceive how the two quantities circuitous in the assay approached zero.

Mr Sven PerssonWhen i bisect by aught on my Mac the calculator says, in swedish, “oรคndligheten” which agency infinity, endlessness. Complete beautiful.

Chris HSince this is not a botheration in mathematics, my accepting would be that the announcer bootless to acquire what they’re accomplishing at Reading. They are allegedly aloof appliance a adapted bulk to represent the aftereffect of abacus by aught in a computer operation and this is allegedly a accessory aberration on the complete adapted bulk NaN (Not a Number) acclimated in amphibian point operations.

domthe Eastern religions got this years ago… its declared ZEN

AndyIn acknowledgment to PK, nulity is allegedly any cardinal you appetite it to equal. I was able Nuffield Physics and the acknowledgment to any botheration was some “magical” or should I say “natural” co-efficent ie PI = 3.?????

JonathanIt makes sense, but all he’s accomplishing is aloof calling one affair (an error), commodity abroad (nullity), which is not at all advantageous in accustomed mathematics (nullity is not a number, like pi or i, it’s every cardinal simultaneously).

JoshuaI get it, annihilation abroad for the annual to abode on so they appoint some guy to achieve up commodity bruised like this to ample in for important stuff. Lol.

Doktor ZeroAccording to my calculators 1/1 is “Error” or “Ma Error”. Is that the aloft affair as that aberrant sign? Sounds easier to use Latin letters… Why didn’t he abode “Ma Error”?

Jason KerwinThis man is acutely mistaken. Has he anytime advised mathematics? I am abashed that he’s teaching his kids commodity a) incorrect and b) that he fabricated up.

DaveComputers are currently able to bisect by zero, and the aftereffect is NaN. (Not a Number) No crashes, no pacemaker deaths. The adequate divide-by-zero botheration is with integers only, and is there for a reason. It speeds up processing if the CPU doesn’t acquire to assay for that achievability and accord with it. While the abyss may acquire some use in mathematics (or it may not, for all I know) I agnosticism we’ll anytime see it implemented in hardware.

Oscar Jenkins, UCDHSCIn any field, assay by x agency multiplication by the multiplicative afflicted of x. So if assay by 0 is defined, afresh there exists some cardinal y such that 0 times y = 1. No such cardinal exists in a field. It follows that this new anatomy is not a field, and therefore, new axioms for assay charge be authentic for this adjustment to achieve faculty and for the notational manipulations to be well-defined. To blanket it up, you cannot absolve the use of acreage axioms if you are not in a field.

By the way …1/0 is not infinity; it is undefined. Also, -1/0 is not abrogating infinity; it is undefined, as well. Any assistant of mathematics with a shread of intelligence will acquaint you that. Furthermore, 0/0 is indeterminate. Do you apperceive what accustomed means? Allegedly not. It agency it cannot be determined. There is a abundant aberration amid amorphous and indeterminate. Mr. Anderson, you should be abashed of yourself for teaching your awry “theories” to schoolchildren. I achievement the university fires you, and your bulk is recinded. Furthermore, this declared assay is about agnate to an applesauce trap; commodity already accustomed to computers and their predecessors, Turing machines.

BradenI accepting this is accession ‘number’ for accepting to assignment with, such as ‘i’ (the aboveboard abject of -1). It will be absorbing to see what they administer to breach with it.

Alex J.So, they aloof invented a cardinal and are animate to altercate us that x/0 is that new number? We charge an infomercial for this… Have you anytime approved to bisect by aught and got an error? Have one or both of your grandparents died because of this? We can’t accompany them aback to activity but… NOW YOU CAN DIVIDE BY ZERO !!! Presenting NULLITY !!! And if you anxiety in the aing 10 minutes, we adeptness accompany aback one of your grandparents (we acquire which one). What are you cat-and-mouse for, anxiety now, now, NOW !!!

BorisOMG YOU CANT DIVIDE BY 0 THIS WILL MAKE THE WORLD GO ASPLODE!!

So basically …… your declared “nullity” lies alfresco the complete and abstruse cardinal lines. If it’s not complete or imaginary, afresh what is? (other than absolutely flawed)

Johnny”Infinity Abrogating Infinity. As anybody knows, annihilation bare itself equals 0″ Not anything. Aloft is undefined. What if the complete aloft had greater magnitude? The botheration with aloft bare aloft is that it is an accustomed form. The botheration with abounding of these equations is that they are declared to according infinity, aback absolutely they are aing it. If I were the ancestor of one of these kids, I would sue the assistant for overextension such bullcrap. The affair of assay by zero, as able-bodied as aloft bare aloft is able-bodied aboveboard in Calculus appliance L’hopitals rule. And as far as pacemakers and airplanes crashing, yeah, it has happened, but I ahead programmers acquire abstruse to t the errors now.

Peter FreemanIt will complete adequate acquire the aloft appulse as the apparatus of aught (Arabia), a absorption that Roman mathematicians did not acquire and apprenticed (along with their difficult abacus system) their algebraic progression. Already the absorption of aught in the cardinal adjustment had been adumbrated and rules about it were discovered, mathematics went a continued way forward.

Eriki ahead this is a big footfall for the mathamatics history. abounding botheration happens all the time aback diveded withe ziro, abounding new technologies for example. able-bodied done Dr anderson. Erik Norway

PeterHaahhaah! The affliction affair is I ahead the guy is serious!! WOW, Annual University seems like a absolutely able uni!!!!!

DavidHow can we acquire his therom if we aren’t alike told what it is and how to achieve it? All this guy is alike adage is that he fabricated up a number. He about pulls algebraic out of nothing! Besides he doesn’t acquire a affidavit for it yet, accordingly authoritative uncertian if all after-effects able are correct. Alike if it does abide and he can do it, and if the “nullity” sits ouside the numberline Computers couldn’tcomprhend it, aback they cannot alike accord with Abstruse numbers.

Ian LangmoreAre you stupid? Looking over his “axioms” on his website (I can’t acquire I did this…) you can see that his abyss is aloof the continued complete band with this added cardinal that comes about whenever you avant-garde approved to do commodity that would aftermath an error. His axioms appearance that already you aftermath a abyss (i.e. applesauce result) there is no way to get rid of it (you can’t bisect it out or decrease it and achieve it go away). So all his “results” could be interpreted as: “lets assignment with the continued reals, afresh if we get an applesauce our acknowledgment is an applesauce we stop” There would be no acumen to abide animate aback from afresh on your acknowledgment is consistently nullity.

MARHis access isn’t alike a theory. A access should accommodate a band-aid to the problem, rather than acquaint added problems. It’s aloof as bad as those cabal theories circulating on the internet.

PeterA lot of bodies achievement acquire been authoritative the annual that 1 / 0 = infinity. This is artlessly not true. It is undefined. Why? because the acknowledgment (infinity) does not accommodated the affirmation of division. Frequently if you booty the aftereffect of a division, the quotient, and afresh accumulate it by the denominator (0 in this case) you get the numerator (1 in this case). 0 times aloft is not 1. In some adapted circumstances, aloft is a advantageous cardinal for 1/0, but not all, and that’s why best CPU’s acquire a way to acquaint the processor to either aftermath a divide-by-zero barring or to set the aftereffect to IEEE-754 infinity.

Rodrigo de Godoy DominguesYes, the absorption is absolutely simple, but added algebraic assay has to be fabricated in adjustment to affidavit the authority of his theory. By the way, it was a able idea. Now, calmly on… :1)

PhilI accepting addled has no lower limit.

i-AnonSo…this guy gives a name to commodity that already has a name, and he gets a annual story? Hey, BBC, can I rename you to UBC and get a annual adventure too? I mean, it’s abandoned fair because you did it for this guy.

Andrew PunchThe anatomy of the botheration with this access is that it is adequate that this new representation will acquire absolutely the aloft restrictions as assay by zero. The botheration with assay by aught is that the aftereffect is “undefined”. Which agency that you can’t use it in consecutive calculations. He would charge to arise up with a authentic proof, agnate to the proofs that are circuitous in circuitous numbers. And aback this is a *maths* botheration not a *computer* botheration I am complete apprehensive that this access comes from a *computer science* researcher.

Jeremy PetzoldCongratulations. I had this Absorption during my cardinal Access for my apprentice but never agitated exploring it aloft autograph a abbreviate abstruse cardboard on the conjecture.

Kevin KadiumWhy would you appetite to devide by aught in the 1st place. Ahead of it logically, Yes it its a algebraic equation, and yes its nice to ahead of a way to breach it. But candidly anybody is right. All your accomplishing is makeing a applesauce bulletin about-face into nullity. Thats not solveing the botheration thats, aloof replaceing an applesauce message. as LJL said, “doesn’t a cardinal lying OFF the cardinal band breach the adage of Completeness?” How can you be teaching this? It’s Rediculous.

Lee”Nullity” is abracadabra for “undefined”

PMwhat botheration of abacus by 0? I abort to see how this is any bigger than demography the complete of a activity as a capricious in the denomenator approaches 0, afterwards all 0 is abundant like infinity, it is not absolutely a cardinal – alike if it is able to be acclimated as one – but a absorption of none. Afterwards all accepting 0 apples is absolutely not accepting any, rather than adage the cardinal of apples I acquire is 0. While accustomed accent would acquiesce for such a annual the absorption abaft it is incomplete. To anxiety 0 a cardinal is not about as incorrect as calling aloft a number, but it absolutely is not as authentic as adage 1. of beforehand that absolutely equals 0.999999999… ๐

TimothyHe absolutely hasn’t aboveboard anything. Assay is consistently antipodal by multiplication. For instance, 4 disconnected by 2 equals 2. And 2 times 2 equals 4. However, If you bisect 4 by 0 and the acknowledgment is “nullity”, afresh that agency you could accumulate “nullity” times aught and get 4. Impossible.

Assumptions for the winso what he aloof accustomed is if we acquire an baffling problem, all we acquire to do is change the name of commodity and it’s solved?

Dave KornDr. Anderson is annihilation but a self-publicist who has fabricated up a new name for commodity that already exists and is now d to acquire invented commodity new. He has done absolutely annihilation of the array and he has invented nothing. Computers acquire been able to represent one disconnected by aught for years; they use the appellation ‘NaN’ (stands for Not A Number) to anxiety it. Saying that 1/0 “sits alfresco the accustomed cardinal line”, as he puts it, is absolutely the aloft as adage that it is not a number. This adventure should never acquire been published. Journalists are meant to assay facts, not aloof acquire whatever they are told by a egoistic third affair and advertisement it afterwards question. Also, accession should acquaint those poor kids that they aren’t the aboriginal at annihilation and their abecedary has been advisedly cryptic them. Come to ahead of it, he should allegedly be addled off for lying to his pupils for the annual of his own claimed advantage.

JenUm, no. You can’t aloof achieve up about rules aback it comes to math. Did he abode a proof?

Mileva MarickSo a new sy aboveboard it all?Interesting…

adelmedicoThere are a few *simple* falsities he writes on his white board. (1) 1 disconnected be aught is not aloft you cannot say 1/0 = infinity. The ogue of assay is a/b = c if and abandoned if there exists a altered cardinal c such that a = b*c. So by adage 1/0 = infinity, he is claiming that 0*infinity=1, REALLY??!! (2)In his affidavit aback he gets bottomward to (1/0)(0/1) = “nullity” he’s aloofness that 1/0 = 1 and according to him, 1/0 = infinity, afresh that band of his affidavit reads as 1*infinity = nullity. Asinine me, I anticipation that 1*infinity = infinity!

Bill MerrillThis doesn’t acquire to be about abacus any cardinal by aught except for the cardinal zero. Therefore, it doesn’t breach anything, unless I’m missing commodity here. If I activate the botheration by allurement about the bulk of 2 aloft to zero, afterward the methods in the video I end up with it equaling 2/2, or 1. Thus, any cardinal aloft to the aught adeptness is one, except zero, which is nullity. Not abiding breadth this gets us….

J. PehkonenYou guys are defining your own algebraic rules for this number, and afresh disproving his access by appliance your own made-up-rules. Remember that in abstruse numbers i^2 = -1. Conceivably abyss additionally has its own algebraic rules? The aloft goes with INF/INF not equaling 1.

KI ahead abyss is the aftermost cardinal in pi!

Scott PerryIf you’ve anytime done any programming, you’ll apperceive this is old news. Abacus by 0 is commodity that programs can be accounting to catch. If they don’t, the computer doesnt aloof die — the Operating Adjustment kills the activity that approved to bisect by 0. It’s not clumsily adamantine to assay your denominators.

HOVISI acquire a problem, I don’t apperceive the answer. I ahead I will aloof achieve one up! Hopefully no one will apprehension if I do lots of apparatus out to abash everyone. The abandoned affair this guy is teaching is how to be creative. Some affair maths is not. Acutely he is not a complete mathematician!

Luke WhitingAny programmer annual his alkali wouldn’t acquiesce a bisect by aught to occour in the aboriginal place! It’s never been complete botheration in avant-garde programming. I ahead this is all a bit silly. “I know. Lets fix a botheration by abacus a new cardinal to the world”.

TomWhen computers bisect by zero, they abide working. x/0 = DivideByZeroException. It’s declared applesauce administration and unless you are one of those idiots autograph } t (DivideByZeroException dbze) { // DO_NOTHING } you will never acquire a botheration

David TurnerTo all you bodies who allocution about diving cakes amid people… Divinding isn’t about how abundant is larboard already you’ve handed out the pieces of cake… Aggravating to administer assay to cake, you don’t say “How abundant is larboard afterwards giving this to X people”, you say “How abundant does anniversary achievement get”… So the division-by-zero botheration in block acceding would be “If you bisect this block amid no people, how abundant block does anniversary achievement get”. At aboriginal Abyss articulate like a able idea, but it’s not absolutely a solution, aloof renaming the problem, as others acquire stated.

AnonI achievement accession is activity to re-educate these poor accouchement afterwards. The BBC should be abashed of themselves for publishing this.

Baron von MannsechsGood job Ranjit–confuse Science vs. Engineering.

Jake Haseman…Infinity anybody?

Catechism Dr. Anderson?”…It is aloof an arithmetical achievement that 1/0 is the bigger cardinal there is…. ” — If 1/0 (infinity) is the bigger cardinal there is… afresh is .5/0 or 2/0 alert and bisected as large? — Does a cardinal bisected of aloft disconnected by aloft prove 2=1? — Why do complete rules about alleviative non-numbers alfresco the cardinal band not administer here?

AnonMy pacemaker disconnected by aught and abyss happened.

GeorgeI abhorrence it aback my bike divides by aught and the brakes stop working.

John GoodHow is the ogue of Abyss altered from that of Infinity? Or for that bulk “Undefined”, which some calculators will discharge out if you try it. I’ve got a bigger name for it: BS

NanThis is some affectionate of joke, right?

Matze M.I admiration how continued it takes until somebody tells them that at the complete position breadth they placed this “nullity” is already (0 – 1*i). But until then, it’s absolutely annual a laugh. Thanks, man. Fabricated this day a funny one.

BobWill this annual Bill Maher to abhorrence and banter practicing Christians, and Catholics in particular, any less?

brynjolfTHis is compleetly wrong. a^0=1 Therefore Nullity = 1

Mathiasok.. this kinda makes sense, but what about infinty disconnected by infinity? Is that 1? I approved to use my texas instruments calucator but it aloof shows an error…

GnomeStep 1. Actualize band-aid 2. Actualize botheration 3. PROFIT!

The New Mathturns out abyss is additionally the aftermost decimal chiffre in pi.

Desperately Gluttonous SenseI get it. I don’t apperceive if it’s clumsily useful, but I get it. If aught is like a void, afresh abyss is like an amaranthine table with abandoned cells. However, already you administer a bulk to it, it becomes complete by any means, accordingly adequate infinity. (unless you can have: [infinity] * 2 ) Maybe that’s for Dr. Anderson to bulk out aing year. I adulation abstruse numbers; they’re like abstruse accompany you can allotment with absolutely acute people.

Daniel AsimovI am a mathematician. Mathematicians acquire been alluringly ambidextrous with assay by 0 for millennia. It shows the massive amateurishness of the BBC Annual Assay that it would not acquire occurred to them to assay with a mathematician afore arbor this abode into a annual broadcast.

Ramesh ArakoniWhy do you decay your time (and mine) publishing such rubbish.. btw.. what we like to anxiety NaN (not a number) has been accustomed a new name and oh.. nullity/nullity= aberration :)

Leo CIt’s my babyish dr. Anderson. You’ve aboveboard annihilation with this theory.

JustinWay to go, you renamed the applesauce message. You still don’t acquire the attributes of infinity, or as you acquire now absitively to anxiety it, “nullity.” From what I’ve read, abyss encompases complete aloft through aught through abrogating infinity, which could additionally be refered to as INFINITY. You aloof declared it by a altered name, you didn’t breach anything.

CS alum studentHoly cow! From what academy and administration did this guy get his PhD? Such blowing and barbarism – Unbelievable. It makes me annual complete mathematicians alike more.

HamidI acquire that the botheration is still not solved, because Dr Anderson considers that aught over aught is according with aught (0/0=0) and he replaced aught with 0/0 in beginning. The achievement is that 0/0 is unknown, and it doesnโt acquire any authentic answer, aught is aloof one acknowledgment of abounding answers to this devision (0/0), this is in bucking with a simple assay like 18/2=9, because in accustomed capacity you get a authentic answer. The botheration with โnothingโ will never breach because โnothingโ is an agreement.

MattWhy did you name undefined?

Richard C. MonglerI disconnected by aught and the cosmos imploded.

stupiditus stupidensisJust aboveboard stupid. I admiration breadth he got his diploma…

Leo CIt’s my babyish dr. Anderson. You’ve aboveboard annihilation with this theory.

AnonSorry guys, this cilia fails. There already is a attribute for 0/0. It’s “O SHI-”

Ian BennettNull is hardly a new concept. Databases has been administration the absorption for years; a acreage which has had no bulk entered, not alike a zero-length string, is ‘null’. A absent acreage has no length, not alike zero. It’s able that accouchement are achievement apparent to the concept.

scottoSo you can breach a algebraic botheration by authoritative up a sym? Wow.

JCI adulation the way all of these ‘non-mathematicians’ use arguments like “If I bisect a pizza amid 0 bodies I haven’t done annihilation to the pizza so I acquire one pizza.” To appearance why it’s wrong, you charge to apprehend that the catechism is wrong. It should be added like this: If I bisect a pizza amidst 5 people, how abundant did anniversary achievement get? A fifth of a pizza. If I bisect a pizza amidst one person, how abundant did that get? One pizza. And afresh you can see logically why you can’t bisect things by aught normally. If I acquire one pizza and bisect it amidst 0 people, how abundant did anniversary achievement get? It can’t be aught pizza, that would betoken there were bodies to get one pizza. It can’t be one pizza either, because cipher is accepting a able pizza. What Dr Anderson says is that if I bisect one pizza amidst aught people, those aught bodies are accepting complete pizzas! It’s laughable.

FrostyI ahead this could acquire able use as a advancement if electronics or computer accidentally bisect by 0, but added than that I don’t see any complete use.

HKewwww, that’s disgusting. Seriously, you absolutely shouldn’t advise accepting annihilation that doesn’t acquire a solid authentic background. It’d be like … teaching creationism.

JImmy RuskaDivision is a activity advised to breach an ascribe appropriately into a set cardinal of pieces. Without giving a authentic cardinal of pieces you appetite your ascribe to be appropriately disconnected into, you are abandoning the purpose of the activity accustomed as division. Replacing an air-conditioned or conflicting bulk briefly with a letter is not commodity novel. There’s no charge to air-conditioned appoint an I over the 0 to be fancy. I can’t see how this is a atypical idea, and I can bet any efforts on algebraic description has been able-bodied exhausted.

don’t absolutely charge to knowdude.. he aloof took out a 1200 blueprint by authoritative 0 devide by 1 b4 he activated powers? the cardinal 1 rocks lol btw thx acquaintance u aloof took bottomward the able of calculus! btw anynumber devided by 0 is either a: not possible, b 1, c 0, d the cardinal itself, e infinity- amuse achieve this a vote bbc!

JCAHas anybody an acumen into what rank the zahlenkoerper of Dr. Adersons’s allegation has?

Erik Schaefer, Madison, WII achievement this gets all-embracing accepting because I appetite to be the aboriginal achievement to acquire the moniker of the abandoned man in Wisconsin who has had sex “nullity” times.

fffomg annihilation is nothing???? MIND = BLOWN

ReidA affidavit of the algebraic aberration of this construction. First we’ll booty what he has accounting about the complete cardinal line. Namely, the reals are the rational and aberrant numbers. Afresh we add in /- aloft to get the continued complete numbers. He afresh writes aloft to be 1/0. This is all we charge to appearance that there is a algebraic aberration which we do presently. Now, aback aloft now can be bidding as a rational, it is an aspect of the rationals. Aback the rationals are a subset of the reals, aloft is an aspect of the complete cardinal adjustment and appropriately is an aspect of the continued complete cardinal system. Thus, we acquire a bucking because aloft is authentic to be both centralized and conflicting to the complete cardinal system. QED

Anonymouscannot bisect by zero world will explode they are apprenticeship kids to draft up the angel by accomplishing ‘math’

/b/The end of the angel is here.

Jordan LundCreating a new abstruse cardinal doesn’t breach the problem, all it does is accredit the botheration an abstruse status.

how embarrasingWhat can we in about-face apprentice from all of this? Avoid embarrasing yourself on an all-embracing calibration by demography 10 annual to go bottomward the anteroom and assay with the algebraic administration to achieve abiding your annual arnt stupid. He could acquire at atomic put his annual up to associate assay afore banishment it on his accepting and affectation it about as mathmatical fact.

Dr Sanford GraceThis man is a blithering idiot!

Ned PetersTell me this is satire. Please, amuse acquaint me this is satire. If it isn’t, afresh whoever wrote this commodity should be accursed and and not accustomed aback into the columnist until he sucesfully completes a aerial academy mathematics course. Or a boilerplate academy one, for that matter.

Magnus MaximusHumankind conflicting aught in the 15th century, which was advised complete footfall in sciense. Now, why does humankind aish zero? Aloof to reinvent it in 1200 years??

SteveThis abyss absorption is meaningless. He hasn’t apparent why it’s useful. Also, it has been agreed that x/0 = infinity, breadth x is any cardinal amid -infinity and infinity, so his affidavit is affecting and hasn’t aboveboard anything. In fact, he has aloof re-iterated commodity that has been accustomed for a continued time, so giving this band-aid a altered attribute agency annihilation

PatrickIf I were to acquire a forumula that had about alternating the ambit an X that is 7/0 and afterwards acquire X*0, the /0 and *0 would aish anniversary added out and I’d get my cardinal back. But if I appraise 7/0 to Nullity, and afresh accumulate it by zero, my cardinal is gone.

Breach at home momRenaming the botheration is NOT a solution. The guy is a complete dingbat.

benjit’s adamantine abundant with 10 numbers to remember I DONT WANNA REMEMBER ANOTHER NUMBER

AhmedYou acquire got to be badinage me. Looking avant-garde to seeing Annual University maths appliance plummit.

nullFunniest BBC commodity ever. I achievement this guy has a lot of accumulation so he can retire to an island somewhere.

asdfdivision is basically subtraction. For example: 4/2 agency how abounding times can you decrease 2 from 4, in this case 4-2=2, 2-2=0 (so the acknowledgment is 2). Now if we attending at assay by zero, for archetype 4/0, this is basically allurement how abounding times can I decrease aught from 4? The acknowledgment is: 4-0=4,4-0=4,4-0=4,4-0=4 …. This goes on forever, it does not end .. acceptation its aloft it is not the bigger cardinal possible. In achievement there is no bigger number. Lets say x = the bigger cardinal possible, afresh what is x 1? As for 0/0, it should according one. Because it asks how abounding times can you booty 0 abroad from 0, 0-0 = 0 (that’s 1 times)

ClemensOkay, but how do you appetite to dividied the new number? I think, afresh there is the aloft botheration again…

RudnickiIf anyone with any algebraic accomplishments was asked to appraise the announcement x/x, they would say that x/x=1. EOF.

The Cool ProfessorIf I acquire 2 marbles and I bisect it over 0 bodies afresh I haven’t absent my marbles, right? I still have’m. But according to mathemagicians I end up with abyss and afar my marbles?

Dr. Andrea ArmaniMark Skerritt answered this botheration (along with all of the bodies who accustomed this affidavit was incorrect) – use Calculus. If this guy is a Dr. in a atone sci department, he should acquire taken calc. and this is the aboriginal botheration that is addressed in any calc beforehand – ytic 0/0 appliance summation. On a ancillary note, Newton developed Calculus. So yes, Newton aboveboard this problem. I don’t apperceive who the added two doctors are who vetted this proof, but they didn’t do a complete able job.

EmanuelThis makes me beam . did he do this for appearance !? ” it’s that easy” …

booty a pissSo what is 10/0? How do you access nullity? does abyss arise afore zero?

Bob”I wrote the able lot bottomward as ytic rules or axioms. Dr. Andrew Adams from Annual University and Dr Norbert Voelker from Essex University helped me beforehand the axioms. Norbert translated the axioms into academy adjustment argumentation and acclimated a computer to prove that they are consistent.” Both of these bodies are computer science “Dr.’s.” Aloof because you can abode your axioms in Prolog doesn’t beggarly it doesn’t belie aggregate we already apperceive about mathematics. Try lambda calculus.

Josh JelinDr. Anderson doesn’t absolutely apperceive what he’s talking about. Defining a cardinal as the band-aid to a botheration doesn’t breach the problem. Mathematicians anticipation of his band-aid hundreds of years ago but instead chose to leave 0/0 amorphous because โnullityโ is useless. This would be absolutely the aloft altercation as adage we โsolvedโ the aboveboard abject of -1 by renaming it to i.

KainawYes – I accustomed it aback in 1978 aback my geometry abecedary explained that it was acclimated to actualize the Cartesian Blueprint (the Y-axis is div0 – a band from abrogating aloft to complete infinity).

ComputerManThe all-embracing accustomed IEEE 754 defines representations for Infinities and for NaNs (Not A Number)s which accomodate Dr. Anderson’s theory. So what’s new? Computers may blast if they haven’t been programmed to acquiesce for these exceptions to the barometer (and not abounding do in my experience) but they could do.

khris777I wouldnt appearance 1st conflicting acquaintance if i had to use complete abecedarian to see it.

Burt WurstheimerThe wurster says: Stupillity. Reduntillity.

FrankIf you would like to do an commodity on me, I additionally ample out a atypical problem.. Appliance the aloft logic, and aggressive by Dr. Anderson. The band-aid to algid fusion. It’s easy! See, E=mc^2. so accumulation can be adapted to energy. To do this, you charge specific distance for the acknowledgment to happen. I acquire arise up with a new appellation “energity”. by abacus accumulation energity = electrical energy! Not abandoned does it aftermath energy, but it is electrical activity rather than calefaction and electromagnetic radiation. This agency no about-face is required, you aloof booty some complete (garbage for instance) and add energity, and you get electrical energy. ambrosial attainable huh? Bigger yet, computers can calmly breach the blueprint afterwards announcement an applesauce message.

ChrisMathematicians acquire been “joining” the ends of the cardinal band with a “point at infinity” for years. It’s an important allotment of the access of egg-shaped cryptography. This is annihilation new – aloof a covering of blanch and a altered name over an complete idea.

A. SupporterI apperceive annihilation about this

dave pIf Dr Anderson insists on putting abyss there, afresh there is no allowance for i. Aish that Circuitous Assay chic matron.

Non ScientistAll this mathematics achievement is great, aloof a abashment best cannot spell. Now there is a ‘real’ problem.

ChristieMajor Blemish in his “problem solving”…he is applying the rules of the complete numbers to a set that is “outside of the complete numbers”. x^0 = 1 in THE REAL NUMBERS aback abyss is NOT A REAL NUMBER you cannot administer the aloft rules!!

IanSo could the assistant amuse explain the backdrop of nulity beneath addition, accession etc…sounds like the “bottom” bulk from filigree access to me … but that’s annihilation new. Next week, Annual Uni discovers set access

Craig BruceThis sounds a lot like what is implemented in IEEE floating-point numbers (which are acclimated on all avant-garde computers), except that it gives “nullity” the name “NaN” for “Not a Number”. NaN operates basically like a allurement in that any operation involving NaN will aftermath NaN as a result. Of course, I don’t absolutely see how you accumulate airplanes aerial aback every flight-control abacus after-effects in NaN or “nullity”.

Stuart Aught disconnected by aught has consistently been authentic as zero. A-level maths. The achievement that computer’s processing microcode doesn’t handle assay by aught is irrelevant. Anybody checks for aught in their cipher and avoids it. Computer Science O Level. So – this alarming adumbration is extraneous to any one with a abstinent education. Well done the BBC – acquire none of you got any Science qualifications?

Abyss MasterBS Access Disconnected by the 0 cardinal of bodies who are digging this adventure equals the abyss adventitious anyone will anytime booty this Dr actively again.

PythagorasWho is this guy who says I can’t breach problems? Heck, I’ve been asleep for added than 2500 years, so breadth does the 1200 years arise in? Go accommodated my acquaintance Giuseppe Peano who aboriginal wrote bottomward the basal axioms of arithmetic. He’ll acquaint you whether there’s a Abyss or not!

nitroxDefine abyss as 42 and you acquire got the acknowledgment to all your x/0 questions ๐

alexthis is retarded… i’ve been ambience nulls for years aback assay is by zero… how does this accede to ytic a problem?

PeteDr. Anderson: I’m abashed as to why you can carbon 0^0 as 0^(1-1) (or why you can alike abode 0^0 at all) from your annual of axioms. Could you carbon this affidavit afterwards any shortcuts and animadversion anniversary band with the adage acclimated from www.bookofparagon.com/Mathematics/PerspexMachineVIII.pdf?

jack welchI ahead he may be on the border of greatness! Nobel prize?

GWBIt’s MMD!!! Mathematics of Accumulation Destruction. We charge now accelerate in the troops.

DBI accede with PK and agnate responses. For some 60 years I acquire consistently accustomed that 0/0 is any number. ‘Nullity’ artlessly agency any number. I would adulation to see any appliance of the absorption of nullity. The accouchement charge be complete confused.

aloof some assistant of physicsIsn’t it attainable – this guy is a lunatic. If he absolutely had commodity new, he would be publishing it in a peer-reviewed algebraic annual rather than aggravating to canvass it to children. My god, are bodies so gullible. I accepting some are, because afterwards all Annual University assassin him, the BBC put him on the news, and the academy at Highdown let him advise their students.

NostradamusI told you this day would come.

KarlDr. Anderson should apprehend “Nonstandard Analysis” by Abraham Robinson. Robinson came up with a connected algebra that active classes of atomic and complete quantities about 50 years ago. Appliance that algebra he showed he could actualize the aloft calculus we all apperceive and love, but afterwards appliance limits.

SekkyThis man is a computer scientist, not a mathematician. I can’t acquire these kids are diplomacy into to this garbage. I additionally can’t acquire that this man can acquire that cipher abroad has anytime anticipation up of giving a new abuse name to an already complete concept, abnormally because how NaN already exists and he is, supposedly, a Doctor of computer science. NaN works well, this is artlessly a addled relabelling. Of beforehand you’ve ‘solved’ it, you authentic it that way in the aboriginal place! I cartel him to accelerate his into MIT, Cambridge or Clay, they’ll shoot him bottomward in seconds. BBC you should be abashed to acquire featured this, apathetic day for annual was it?

Cameron Kenneth KnightAlthough I do not acquire that Dr. Anderson’s access holds water, to the bodies who ask to appearance the cardinal in bifold absolutely charge to absorption the IEEE-754 standard. The IEEE-754 accustomed specifies bifold representations to 32, 64, 43, and 79-bit floating-point numbers. In this blueprint allows for the numbers infinity, -infinity, and NaN. Aback NaN is about what Dr. Anderson descibes as nullity, one could use that as its repesentation. Also, NaN is authentic aback the backer is 2^e − 1 and the mantissa is non-zero, which covers many, abounding numbers. One could instead ascertain NaN to be breadth the mantissa is non-zero, non-1 and abyss to be breadth mantissa is 1. Integer representation of abyss (and additionally aloft and -infinity) is about not needed, although if you were to use a adapted accumulation set, it could be done. E.g. attractive at an 8-bit accumulation about authentic as -128 to 127, one could ascertain 127 as infinity, -127 as -infinity, and -128 as nullity.

[email protected] of the bodies bashing this should apprentice some basal maths. Others should apprehend the affidavit he has written. Still others should apprentice to apprehend the aboriginal band of the commodity above, which is adequately ablaze that Dr Andersen works at a university, and not a school. Abominably the ill-informed comments so outweigh any advantageous criticism it is adamantine to acquisition genuine, sensible, objections. Those with animate objections would allegedly be best adequate to coursing bottomward Dr Andersen’s email and present them to him – so far none of the mathematicians who acquire approved acquire managed to appearance there is annihilation amiss with transreal mathematics (well… I acicular out that his beforehand adjustment was defective abrogating infinity) The comments about NaN about abash aloft with what Dr Andersen is calling nullity. Some programming languages ascertain infinities as well, however, and from this bend I acquire some of the criticisms are valid.

KnightRiderIs he suggesting that coconuts migrate?

Algebraic GuySad absorption on the accompaniment of authentic bookishness in journalism (which seems to be afterpiece to aught than to abyss ;-). Why alike anxiety absorption to this vapid, abandoned access (not to acknowledgment the air-conditioned claims that the botheration was ‘unsolved’). If anything, the botheration was ignored, because it is of no significance. Shame on you BBC.

Mark Wagner”Nullity” is hardly a new absorption in computing. The IEEE accustomed for computer mathematics defines three “non-numbers” that can aftereffect from an operation: complete aloft (the departure of 90 degrees, or 1/0, or any of a cardinal of added operations), abrogating aloft (the departure of -90 degrees, or -1/0, or any of a cardinal of added operations), and not a cardinal (0/0, or infinity/0, or -infinity/0, or added operations that are not well-defined). Calculus-level mathematics has been able to accord with 0/0 for a little over three hundred years. It all depends on breadth the zeroes arise from: 0/0 could be 0, or 17, or any added number. There’s a abode declared L’Hopital’s aphorism for chargeless this.

SpicemakerMany of the operations Dr. Anderson performs to “prove” this (such as the algebraic accepting that (a/b)^{-1} = (b/a) ) _assume_ the basal acreage axioms. Of course, these axioms acquire that aa^{-1} = 1 abandoned if a ≠ 0. Dr. Anderson aboriginal has to appearance that if you extend the acreage axioms to accommodate 0^{-1}, afresh the accustomed algebra applies to it. And he hasn’t.

JBSee www.jamesanderson.co.uk for James Anderson the acreage abettor (top of the annual beneath Google). Now all becomes clear!

DanMahesh Sooriarachchi, what you adduce is (an apple)/0 = (an apple) which agency basically that 0 = 1. Which bigger not be the case. abacus by 0 cannot abide or algebraic doesnt work.

Ashley ColeI am currently belief mathematics at A level, and this cannot be real. Absolutely he cannot jsut achieve up a new number? If annihilation it should be beneath abstruse numbers? I disagree with what Dr James Anderson has proposed, as you cannot bisect any cardinal by zero, as there is annihilation there to be disconnected by! It cannot be done.

terrySo he formed out that the aught to the adeptness of aught was aught and gave it a name?

John MeagherDr Anderson may acquire the adapted idea, but the allotment assemblage is a little off. According to Dr. Anderson, aback you bisect by zero, your acknowledgment goes to aloft ( /-), and covers a ambit of numbers starting with the aing cardinal aloft the numerator to infinity. However, “nullity” indicates a NOT anything, alike admitting abacus by 0 is a NOT NULL answer. I’m not a algebraic wiz, but it would achieve faculty to me if abacus by aught is still a controversy, afresh “nullity” would be a “not defined”. By agreement “nullity” alfresco of the cardinal line, indicates the acknowledgment is still unknown. If the acknowledgment is unknown, afresh “nullity”, with all that the name implies would be an inappropriate name. “nullity” would be appropriate, if the affect of abacus by aught after-effects in aught (null). This tends to achieve added faculty to me: 0 x 5 = 0 0/0 x 5/0 = 0/0 5/0 = (0/0) / (0/0) 5/0 = 0 If 0 follows the behavior of babyish numbers, afresh the acknowledgment is infinity. If 0 is advised as null, afresh abacus by absent is the aloft as abacus by 1; No affect on numerator as a accustomed cardinal over one. In either of these cases, “nullity” is not an adapted name for a not-null result.

Abandon NorrisOnly Abandon Norris could bisect by zero. And I’ve done it twice.

HihoWhat a agglomeration of baloney! The botheration with 0/0 and 0^0 is one of uniqueness, not of artlessly defective a name for them.

jbuddenhmy agenda camera tries to bisect by aught absolutely often, i acquire to booty the array out and reinsert it as a workaround. dr anderson’s simpler band-aid would save me that trouble! he should let nikon apperceive quickly!

Ex of ReadingMessage for Kevin Warwick: Be afraid, be complete afraid!

HenryThe botheration is that abacus by aught is not a problem. It’s not an operation, aloof as jumping afterwards appropriation your anxiety off the arena is not jumping, or bistro afterwards aperture your aperture is not eating.

StephenThis is complete crap. Of beforehand the accepting are confused. It’s absolutely wrong! I can assemble a all-inclusive cardinal of examples breadth 0^0 is one, or zero, or one half, or a array of added values. Can I compute commodity with this “nullity”? I ahead not. 0/0 is an amorphous form, and there are an complete cardinal of attainable ethics for it. This is annihilation but some computer science PhD delving into the angel of cardinal access aback he absolutely shouldn’t, and all it is activity to do is abash the accepting he teaches, abnormally aback they get to a complete maths class.

NuriThe Complete Numbers anatomy a complete ordered field. Let’s aloof attending at how able-bodied Abyss fits into the Complete Field. FIELD INCONSISTENCY The Complete Numbers anatomy a field. In it, every cardinal except the additive/multiplicitive appearance has a altered audible afflicted aspect such that x*x`=E. What is nullity’s inverse? Let’s attending at the multiplicitive inverse. Nullity’s multiplicitive afflicted would be 0/0 (it’s reciprocal). By this result, either E=Nullity=0 or Abyss is not in the set of Complete Numbers. If it is not in the set of Complete Numbers, what set, group, ring, field, algebra does Abyss fit into? Would 10 Years kids be able to a abstracted set of rules audible from the rules they’ve abstruse thusfar? There’s a acumen this assistant is teaching aerial academy children… That acumen is not flattering.

my nameand the aboveboard abject of -1? i’ll anxiety it bob! it lies off the numberline, and i’ve aloof aboveboard an age-old problem. appetite to accompany the ytic fun? aloof rename everything! it’s easy!

PeteHow about encoding the video in a architecture that’s not as abandoned a $0/0… MPEG is an industry standard.

EisenfostThe aing affectation for 1/0, afterwards Nullity, shall be Willy-Nilly!

Flash Cutnullity =NaN(Not a Number) Do you ahead bodies are stupied???????????? Try afresh .LOL

Percival SittingbourneThat’s Numberwang!

ArturitoUhhh, Riemann Sphere? This guy is 150 yrs slow.

O RamonIf you acquire abyss over nullity, does this beggarly that it is according to 1? or would it abide alfresco the cardinal series. If you accumulate abyss by any complete cardinal is it still a complete number, or is it nullity? If you accumulate a abyss by an abstruse number, it it in either or both sets?

MaczComputers acquire this absorption already. It is declared NaN. This guy should not be accustomed to teach. His axioms=diddly/squat.

Eric (M.S. Mathematics)I had an uncle who was a aesthetics profressor (now deceased). For entertainment, he acclimated to beforehand that there was an added accumulation about amid 8 and 9. He’d acquaint anybody he was animate on a affidavit declared “the sneak” whereby he planned to band up 10 oranges and then, somehow, “sneak” the added orange about amid the 8th and 9th one, appropriately proving there is an added accumulation in there somewhere. He’d acquaint bodies about this and beam until he had tears in eyes. Yet, somehow, his mathematics are added ambrosial to me than Dr. Anderson’s. At atomic they’re funny.

coyotethis is not a cogent ‘discovery’ and should be peer-reviewed. his ancestry [shown in video] contains two abeyant meanings for 1/0. the aboriginal is his infinity. the additional is to abstain it while accomplishing his ‘solution’, he says that 0/1 x 1/0 = nullity… this is cryptic accustomed his above-mentioned ogue of aloft achievement 1/0. now, aloft altered by aught is nullity. on a ancillary note. i would like to see his adjustment of accustomed algebra appliance nullity. 37/0 for instance. 37/0 = 37/1 x 1/0 = 37 x aloft … but 37/0 is 1/0 x 0/1 x 37… this seems to be not acutely authentic in acceding of behavior. this seems ambiguous as we are now aback to the aboriginal assay by aught achievement amorphous if multiplication is not consistent.

Erik MesoyThis has added holes in than Swiss cheese. By his math, 1 = 1/1 = (1/0)*(0/1) = (1/1)*(0/0) = 1*Nullity. Appropriately abyss charge be the multiplicative appearance element, nullity=1. I additionally agenda that this is filed beneath “people” not “science”, and the man does not acquire a algebraic bulk but a atone sci degree. Another hole: (a/b)/(c/d) = (ad)/(bc), so (0/0)/(0/0) = (0*0)/(0*0), and thereby nullity/nullity = nullity. Bisect by abyss on either ancillary and you get nullity=1, accumulate by abyss on either ancillary and you get nullity=nullity^2. Also, this breach algebraic groups and rings too. 1 nullity=? 1*nullity=? 0*nullity=?

PWebinfinity/infinity is not according to 1 any added than infinity-infinity=0 . Aloft cannot be advised like a approved number. Aloof because we don’t apperceive what nullity/nullity is doesn’t beggarly the absorption is pointless. Let the authentic association array it out afore you all bedraggled your pants in frustration.

Disgusted in VegasHe’s absolutely teaching this to accepting as accustomed “mathematics”?

ZenoThis is a bulk of crap. Adage abacus by aught after-effects in commodity that is not a cardinal (nullity) solves annihilation and breach algebraic closure. It is abject that this idiot is accustomed to spiral all those kids up. If he has a bulk in mathematics it should be afresh revoked, as able-bodied as his teaching credentials.

Chargeless Will ::= Nullity In his works, Mr. Anderson proposes that a “free will like ours” does absolutely exist. If so, afresh abyss absolutely does exist. However, both are aloof artificially authoritative up commodity that is absolutely undefined. No botheration solved, abandoned adjourned to a aing apery some instance of nullity.

Nick WilsonWhat ‘problem’ is acquired by assay by blank achievement undefined? How does this admonition annihilation in any way? You can trivially ascertain it any way you like, but so what? This causes big problems – his axioms charge be a complete afterlight of all our basal arithmetic. This is complete stupid. PS lots of bodies acquire to ahead (oddly) that 1/0 = aloft — THIS IS NOT TRUE. 1/0 != infinity. It is undefined. lim_{x rightarrow 0} =infinity (in words: the complete of 1/x as x tends to 0 is “infinity”, but has NO VALUE at x=0) We use a lot of altered annual aback we allocution about “infinity”. The calculus absorption of an arbitrarily ample cardinal (ie ‘limit as x tends to infity’ or ‘1/x tends to infinty as x tends to 0’) is altered from the absorption of, for the instance, the cardinal band achievement “infinite”. The transfinite numbers (aleph_{0}, etc…) are yet accession altered acceptation of the chat infinity. Did this idiot get his Doctorate in Geography or something? I can’t acquire no-one has told him that throwing an barring on assay by aught is able – would we rather acquire the alike plough into the arena because it ignores the error? Communicable exceptions is able software design, not blank the botheration by renaming it.

jhughsResponding to “Pythagoras'” catechism about whether or not 2/0 is alert as complete as 1/0. Although I don’t apperceive absolutely if that’s correct, it is mathematically complete to say that some complete sets are aloft than others. Accede the afterward three sets of integers: a) 0 to infinity; b) 0 to -infinity; and c) -infinity to infinity. If you ahead of it in acceding of the ambit growing abroad from 0 afresh it’s ablaze that set “c” is alert as big as either set “a” or “b”. An alike added abashing archetype is the set of integers from 0 to aloft adjoin complete numbers amid 0 and 1. If the aboriginal set grows at the bulk of 1 accumulation at a time, but the complete cardinal set grows by behindhand (ie, 0 & 1, 0 .5 1, 0 .25 .5 .75 1, etc.) afresh the set of complete numbers not abandoned grows faster than the integers but it grows consistently faster. And so, it is a achievement that some complete sets are aloft than others. I know, it threw me off at aboriginal too, but now it seems reasonable (which is able or I would acquire bootless the chic breadth we abstruse that – although now it abandoned comes in attainable for d off).

Captain AnonInsanity! 1/2 is agnate to 1*(1/2) 2/2 is agnate to 2*(1/2) 0/2 is agnate to 0*(1/2) Now m/n is agnate to m*(1/n) 0/0 is agnate to 0*(1/0) Everyone knows 0 * (anything) is 0. So, “anything” includes all numbers, complete and imaginary. a. 1/0 = infinity b. 0*(1/0) = 0*infinity c. 0*inifity = 0 Hello?

MOVThat makes no faculty at all. 0^0 is not defined, accordingly 0/0 is not defined. You can’t prove annihilation by ambagious bodies with amiss facts.

ZenaMakes calculus a able lot easier too. lim(x->0) x/sin(x) = 0/0 = NULLITY!! Oops. Looks like we’ll acquire to carbon all the algebraic books in the able 500 years.

Wlymsksprmuch ado about annihilation

Egon IpseThis is funny! To all bodies announcement here: YHBT. YL. HAND! Just attending at his beam on the video aback he claims that the alternate or 0 is 1.

RamanujanI achievement Dr Anderson gets a huge budgetary award-winning for his assay so he can retire and stop teaching children. What a shame, breadth this angel is going…

Anony!OK he’s aloof a complete newb at comp-sci algebraic assistant who anticipation he came up with commodity original. I’d bet it wasn’t his absorption to go to the media, though. Computers CAN represent -/ infinity, and about do. Also, what is aloft * 0? ZERO. That’s why abacus by aught makes no sense, aback assay is the ytic antipodal to multiplication. The botheration this commodity raises is absolutely what affectionate of applesauce our academy systems can shouvel to kids. I am not religous, but I was able at academy that change was “THE WAY” alike admitting it’s aloof a THEORY, and I’m ambrosial abuse abiding that’s not how authentic scientists would appetite it.

RPGreat. This guy has spent all his time advancing up with accession attribute for infinity. I could aftermath an appropriately abortive sym, oneity, for the aftereffect of a cardinal disconnected by itself. Is that groundbreaking? However, I acquire it does annual for all those times planes acquire abandoned out of the air. It wasn’t aerial turbulence or some array of storm. The alike artlessly approved to bisect by zero.

Steve Q.All maths problems are calmly aboveboard if one wishes to artlessly achieve up a new appearance to abode on the adapted duke side.

ChrisSo, acquaint us added numbers on this new cardinal line, sir! You’ve accustomed us a cardinal that can be any added cardinal (as breadth x is any cardinal x*0=0, so 0/0=x, which agency nullity=any number). How about a cardinal that can do backflips? Or a cardinal that can about-face invisible?

SumDude”which solves maths problems neither Newton nor Pythagoras could conquer” How ridiculous! The acumen neither Newton nor Pythagoras “conquered” this botheration is because is because it has already been solved. 0/0 is amorphous and calling it abyss does not change anything. How does this “new” access of his accommodate a new acknowledgment for 5 * (0 / 0)? The abandoned change now is that instead of accepting “division by zero” computer exceptions one would get “arithmetic involving nullity” exception.

CarlosThere already is a name for this number: QNAN Abyss is aloof a bad name that implies the adverse of what it is. A bigger name would be afflicted nullity.

What happens aback you assume…First of all, don’t assurance a mathematician who issues apocryphal statements. 1/0 is not according to infinity; ogously -1/0 is not according to abrogating infinity. If we appetite to compute 1/0, we do this by demography the complete of 1/x as x approaches 0. So let x = 1, 1/2, 1/5, 1/10,000,… Acutely 1/x gets inifinitely ample as x approaches 0. But what if we access 0 from the added ancillary (the larboard limit)? Aback you let x = -1, -1/2, -1/5, -1/10,000,…, afresh the complete of 1/0 approaches abrogating infinity. Aback the larboard complete and adapted complete of 1/x as x approaches 0 do not agree, we cannot say that 1/0 equals anything. (Want to annual it? A agnate archetype would be the blueprint of the departure function. Acquaint me what the complete of tan(x) is at pi/2 radians, or 90 degrees.)

EdwinI invented the cardinal 5. Bodies acquire to like it.

J. A. O. EkbergThe botheration with this is not that it’s amiss or abortive (it’s not). It’s aloof that admitting I acquire never aboveboard bookish affidavit of it before, cipher anytime acutely doubted that arithmetics including infty, -infty and “indeterminate” can be axiomatized. Talking about such things at schools is not a bad idea; renaming “indeterminate” into “nullity” and claiming this is commodity revolutionizing is absolutely accession thing. In acceding of change (though not usefulness, perhaps), Jesper Carlstrรถm’s caster access is abundant added interesting.

Ron LarhamComputers can bisect by aught if the accession is implemented correctly, 0/0=nan, 1/0=inf, … by the way nan agency not-a-number.

Jim BelcherThis is too abundant of a abstruse abstraction. The affidavit of its authority is adequate to lie in award a activated authentic application. Mathematicians are apperceive for abstruse annual that are proovable abandoned on the blackboard. OK, so we can do it on paper, so what?

cwm9Every mathematically absorbed achievement is allegedly groaning adapted about now. This is complete . The theories of 0/0 acquire been formed out for ages — there’s no abstruseness here. You can’t apperceive annihilation about 0/0, you can abandoned say commodity about the complete as you access this accompaniment from alternating a connected line. Go attending up L’Hopital’s rule. You can’t alike say infinity”nullity. Heck, you can’t alike say infinity=infinity. There are altered classes of infinity. About the abandoned acceptation “nullity” could acquire that would be reasonable is “undefined.” Which, OMG, has already been acclimated to ascertain this state. About the best he could be accustomed for is inventing a new attribute for the chat “undefined”. Complete rubbish.

NicholasThis guy is aloof allotment a attribute to commodity that still isn’t a number. It’s like me renaming the Sasquatch a “writing desk”, pointing to a desk, and claiming that it’s affidavit that the Sasquatch exists.

Adam Setzler1/0 = Infinity 23/0 = Infinity 37/0 = Infinity 419/0 = Infinity 2305/0 = Infinity 12904/0 = Infinity 349002/0 = Infinity . . . Infinity/0 = Infinity Infinity = Infinity Your mom.

Cambridge Maths PhDHaving aloof apprehend his papers, (and as added bodies acquire suggested) the attribute Phi is annihilation added than a autograph for “undefined”. He lists his axioms which are calmly accustomed with this understanding. This absolutely is a second-rate allotment of work. FORTRAN already uses the adjustment he is advocating (Phi=NaN).

DavisHint to the BBC — allocution to an complete mathematician afore publishing such a abominable piece. We’re absolutely absolutely approachable, and altogether adored to explain why this is silly.

RayDr. Anderson acutely knows annihilation of avant-garde algebra. There is a complete authentic acumen why assay by 0 is impossible, and if he wishes to achieve it attainable he charge additionally be accommodating to acquisition a backup for the foundations of abundant of mathematics. The complete cardinal band is a field, and it is not attainable to acquire assay by zero, the accretion identity, in a nontrivial field. You can’t aloof achieve up a new attribute and achieve a scattering of asinine operations on it to breach a “1200-year old problem”. If he wishes to be taken actively in the annex of mathematics, he charge accommodate a radically new algebraic anatomy aural which his abyss may exist. I don’t affirmation that such a ability is impossible, but until it is accomplished, his “result” is casuistic and should be labeled as pseudomath.

MikeThis is a able assignment for all who listens to “scientists” who deliver all-around warming… Acknowledgment assistant

AnonThis is complete crap. Who hasn’t anticipation about replacing the absorption of assay by aught with some attribute while they were acquirements about replacing the aboveboard abject of abrogating one with i? If this is a breakthrough, I should booty over this guy’s job. At atomic i has applications in the complete world.

Absolutely ConfusedSo James; you say: 0^0 = 0^(1-1) = 0^1*0^(-1) = … = nullity. What about: 0 = 0^1 = 0^(2-1) = 0^2*0^(-1) = (0*0)*0^(-1) = 0*0^(-1) = 0^1*0^(-1) = … = nullity.

Adammost computer programs will t the Assay By Aught applesauce and assassinate cipher advised accurately for such an eventuality. It’s complete complete air-conditioned that programs will blast airplanes or stop a assault affection aloof because it hit a Assay By Aught error. Software testers consistently assay this aftereffect and watch how the software behaves able-bodied afore it goes to market. All Dr. Anderson did was put a name to a absorption that’s contrarily accustomed as the Assay By Zero.

YabaTheWhatSomehow this able commodity feels like a artifice to get added bodies to do Dr. Anderson’s job for him. Abundant bodies acquire acicular out the flaws in the apparatus of “nullity”, and a few acquire adapted added able anatomic alternatives (such as my beforehand one, apparent beneath because accession had the ablaze absorption of announcement replies in about-face order). Accumulate an eye out, as he may advertisement a cardboard in a year or two demography acclaim for annual that appeared in replies to this article.

[Using the end of this bulletin to see if HTML cipher may be buried afresh into responses to actualize paragraphs. Artlessly accounting accustomed allotment doesn’t work.]

Paul WellsEveryone should apperceive that the BBC abandoned cast arts and bendable science programmes – so advertisement commodity like this makes them feel they acquire maths.

Andrew P.I’m no mathemetician, but aloof at aboriginal glance I acquire problems with this. I accepting one of my bigger “problems” with this…is that he appears to be alleviative aloft as a number. Aloft is not a number, but a concept. He has that 1/0 = aloft and -1/0 = -infinity. That’s not absolutely right, because it’s actually: lim x->0 for 1/x = infinity and lim x->0- for 1/x = -infinity But at x = 0, 1/x is undefined. There is no simple algebraic blueprint (a b, a-b, a*b, or a/b) such that the acknowledgment is “infinity”. If you afresh altercate that appliance banned you can say that his axioms hold…I would afresh disagree…because lim x->0 for 1/x = aloft AND -infinity (depending on which way you access zero). (same for -1/x) If you do adjudge to activity aloft as an complete number, afresh the abandoned way his axioms absolutely authority is if aloft = -infinity…so that agency 1 = -1. (not to acknowledgment amaranthine added areas breadth alleviative aloft as a cardinal messes things up…)… So if the axioms don’t hold, well, annihilation you use those axioms in absolutely doesn’t authority abundant water…If i’m amiss on this, feel chargeless to complete me…

Jeff PeggThis is the stupidest affair that anytime got attention! Period! You aren’t accomplishing annihilation innovative, you are aloof aggravating to get your name into the books. And a adduce from the commodity is the worst. ”We’re the aboriginal schoolkids to be able to do it – that’s absolutely cool,” added another. You are like the aboriginal christians to be deceived.

bjrThere’s too abounding comments allegory i (sqrt(-1)) to this new Abyss concept. The difference, of course, is that factors i can be advised as a audible point on a cartesian alike (it represents the non-real boxlike roots, which are advantageous in ytic some problems) admitting abyss would be advised by colouring the complete cartesian plane. There’s lots of added high-fallutin’ words aerial about achievement too: non-euclidean geometry, transreal arithmetic. If this achievement is so abstruse that accession with an undergraduate accomplishments in mathmatics can’t see how it applies to problems he’s accustomed with solving, why primary academy pupils? Acquire they acquire acquired some amazing capabilities which acquiesce them to administer non-real mathematics to the complete world? Or does it aloof achieve a admirable annual to barrage this non-practical theory?

PMMy aboriginal botheration is his accepting that 1/0 equals infinity, and -1/0 equals abrogating infinity. 1/0 does not according infinity. 1 disconnected by an infinitesimally babyish complete cardinal is according to infinity. 0 is not an infinitesimally babyish number. To achieve a accidental example, accede the accumulation of an “object”. If the commodity has an infinitesimally babyish accumulation and a nominal volume, its specific aggregate (inverse of density) is appreciably ample (approching aloft as the accumulation gets smaller). If the commodity has a accumulation of 0, THERE IS NO OBJECT. Appropriately a distance like specific aggregate would be undefined, because the commodity doesn’t exist.

Anonomous cowardThis is absolutely the aloft as adage that the aboveboard abject of -1 is i or whatever abroad you anxiety it. It would be easier to aloof accumulate it as (0/0) in equations afterwards giving it a attribute (that is already in use). Decay of time.

…really?With the adapted assumptions you can prove annihilation to be true…even if it’s absolutely apocryphal and/or inconsequential. 1/0 is not infinity. 1/x as x approaches 0 is infinity. They are two complete altered things. Adulterated accepting = air-conditioned proof.

John MeagherDr Anderson may acquire the adapted idea, but the allotment assemblage is a little off. According to Dr. Anderson, aback you bisect by zero, your acknowledgment goes to aloft ( /-), and covers a ambit of numbers starting with the aing cardinal aloft the numerator to infinity. However, “nullity” indicates a NOT anything, alike admitting abacus by 0 is a NOT NULL answer. I’m not a algebraic wiz, but it would achieve faculty to me if abacus by aught is still a controversy, afresh “nullity” would be a “not defined”. By agreement “nullity” alfresco of the cardinal line, indicates the acknowledgment is still unknown. If the acknowledgment is unknown, afresh “nullity”, with all that the name implies would be an inappropriate name. “nullity” would be appropriate, if the affect of abacus by aught after-effects in aught (null). This tends to achieve added faculty to me: 0 x 5 = 0 0/0 x 5/0 = 0/0 5/0 = (0/0) / (0/0) 5/0 = 0 If 0 follows the behavior of babyish numbers, afresh the acknowledgment is infinity. If 0 is advised as null, afresh abacus by absent is the aloft as abacus by 1; No affect on numerator as a accustomed cardinal over one. In either of these cases, “nullity” is not an adapted name for a not-null result.

Nathanso if a planes computer adjustment divides by aught and crashes, we’re all gonna die BUT! if it divides by abyss and crashes, we’re all gonna die. wait…

JamesMany bodies announcement achievement are d a lot of benightedness about mathematics. It has been accustomed for a continued time that 1/0 = aloft and 0/0 is undefined. Accustomed computer accession can not cope with this. What Dr Anderson has arise up with is a adjustment for accepting computers to do computations involving these operations. However, it is so attainable that I agnosticism it has not been done before.

James HA lot of bodies announcement achievement are d a lot of benightedness about mathematics. It has been accustomed for a continued time that 1/0 = aloft and 0/0 is undefined. Accustomed computer accession can not cope with this. What Dr Anderson has arise up with is a adjustment for accepting computers to do computations involving these operations. However, it is so attainable that I agnosticism it has not been done before.

JamesA lot of bodies announcement achievement are d a lot of benightedness about mathematics. It has been accustomed for a continued time that 1/0 = aloft and 0/0 is undefined. Accustomed computer accession can not cope with this. What Dr Anderson has arise up with is a adjustment for accepting computers to do computations involving these operations. However, it is so attainable that I agnosticism it has not been done before.

Infinty and BeyondThroughout history the blueprint (n/0) = infinity. Absolutely he has aloof afflicted the name accustomed it a new sym. PS can i acquire a reserch admission for advertent this asset of information.

Reid NicholAll this guy has done is redefine what the complete cardinal band is and a few numbers. Let’s go over his aloft mistake: inf neq 1/0 To get this one charge do: lim_{x->0^ } 1/x Similarly for -inf. But one charge agenda that if we access 0 from the larboard afresh the assurance flips. But that’s accession story. What he did was an operation that was amorphous and ascertain it afterwards exploring any of the implications. This guy is arena with a NEW cardinal band of his own invention. Also, this NEW cardinal band has not been apparent to be mathematically connected in any way appearance or form. This guy should be abashed to advertisement this.

Mr. ner axiomnullity = all the peoples in this blog.

auto driverGet a complete job giving handouts to immigrants instead of crumbling your time growing a bristles and blurred like an Attainable University presenter on BBC 2 in 1983.

A BritWhat is math?

BeauThese poor kids. I aloof achievement none of them put this on their academy applications beneath accomplishments.

GregorySo.. it took this continued to ad-lib accession abstruse number? The aboveboard abject of -1 is “i”, and now we acquire another. I don’t see annihilation big in this, aloof semantic gymnastics. Able-bodied done to this guy for diplomacy it able-bodied though…

Added dimension?The cardinal band is linear. Add accession band and two cardinal ambit gives us two dimensions. And assuredly add a third and there is our 3rd dimension. Now according to this ”But Dr Anderson has arise up with a access that proposes a new cardinal – ‘nullity’ – which sits alfresco the accustomed cardinal band (stretching from abrogating infinity, through zero, to complete infinity).” So does this beggarly he activate an conflicting dimension?

Dan JonesMy calculator doesn’t accord me an applesauce aback I bisect by zero, it aloof allotment “undef.” It looks like Texas Instrument ample out the band-aid continued afore this crackpot!

Patrick WeberHis estimation is absolutely alfresco of the rules of mathematics1 How can this be useful1 If the final acknowledgment to a botheration is “nullity” what does that mean1 Does it get us any afterpiece to compassionate than 0/0; no1 What is “nullity” times 4- He had kids acquire that 0/0 could be accounting as a 0 with an I through it1 They acquire done annihilation that Newton couldn’t1 Throughout this column I acquire been appliance 1’s in abode of periods and -‘s instead of catechism marks1 I aloof basal to let you apperceive that I acquire done commodity that Shakespeare never could1 I am awesome1

Ian BremnerHardly annual aback mathematicians acquire been usng a agnate adjustment to represent the aboveboard roots of abrogating numbers, at atomic they’re hones about it and ascertain the abject of any abrogating cardinal as ‘i’ – abbreviate for ‘imaginary’

AnonI am but a adolescent and ahead like a child. I am told that to breach the blueprint 2x = 4, I can bisect by 2 to get x = 2. Appropriately 2 times 2 = 4. Now I am told that I can bisect by zero. Dr Anderson says so. So to breach the blueprint 0x = 1, I charge bisect by aught to get x = infinity. So 0 times aloft is 1. Now let me breach the blueprint 0x = 2. Afresh I get x = infinity. So 0 times aloft is 2. Now let me think. Oh yes afresh 2 = 0 time aloft = 1. Oops! Amuse Sir, what acquire I done wrong.

ErikIf this man thinks he is some array of algebraic prodigy, he needs to go booty his medication. And teaching this ‘stuff’ to kids is aloof outrageous. He doesn’t absolutely DO annihilation added than say 0/0=0/0 and afresh accord it a name, ha. What a joke.

BaruchThis doesn’t achieve sense. “Nullity” and aught may be altered entities, but aught is the cardinal that appears on the cardinal line.

SoerenHe aloof “solved” the case 0/0, but not n/0 by appliance (valid) algebra rules. His “proof” is like adage “8/4” equals 2, so aggregate abroad disconnected by 4 equals 2. This “nullity” is aloof accession alias for 0/0, which has been invented many, abounding times before.

derpyeah because ya know, authoritative your own “number” up and adage it’s a band-aid is absolutely mathematical.

DumbStruckIf one of his pupils came up with that in class, I am abiding Dr James Anderson whould of told them off for crumbling time. The accession name to Abyss is declared Stupidity.

AbhiWhats the aberration amid aloft and aught absolutely ?

ZYour calculus assistant would be complete sad. =( Please advise the kids complete mathematics and not some hoopla. Don’t decay their time.

APBIf anyone has apprehend bottomward this far… I acquire ‘Sam’ has it. In the “Proof”, which is added of a array of verification, (1/0)*(0/1)=0. But (1/0) is Nullity. So, in essence, he’s appliance Abyss to prove Nullity. A big no-no.

CordeliaWhy does the attribute for abyss attending like a basal phi? And this is absurd.

Abashed at MeaningHow about we aloof ascertain 0^0 as some number? Afresh I can prove that 0^0 is that cardinal that we defined. Yeay, I aloof aboveboard the 0^0 problem.

MMI’ve aboveboard an commodity on BBC adage that UK does not acquire abundant scientists but I didn’t able until now that it was such a huge botheration …

Lost?Sorry, at what date did this become annual worthy? Who absolutely went out and scouted this story? Is this the aing of TV, Web, Radio accustomed diplomacy and annual programming? Dump this blah and abode on commodity that absolutely MATTERS! Otherwise I abhorrence we will all end up achievement disconnected by aught into an complete accompaniment of aloofness and atheism arise the acutely anytime accretion “anything โul do” annual culture….

h_mMaking up pretend numbers = I ARE MATH SMARTNESS. I hereby adduce a new cardinal that is to be declared “squnch.” It has a bulk of 23, -78, Pi, and the blush orange; simultaneously. Also, it is lemon-scented. I doubtable that the able use of Squnchificonics will be able to breach all sorts of avant-garde air-conditioned algebraic problems, as able-bodied as abrogation abaft a fresh, aesthetic scent. Grant money now plx.

PythagorasBy the way, I lived about 500BC, so the botheration is added than 1200 years old. Added than that, I can’t accountability this article.

Rusty ShacklefordWhat an complete decay of electromagnetic activity this adventure is appliance adapted now. Amazing. I ambition my bang-up formed at the BBC.

MarkHow does this adapt from i=SQRT -1, i is an abstruse cardinal ??? Used in Calculus for YEARS !!!

Bryan WagnerThis access is like arena a d of “I win”. Here’s a all-encompassing algorithm: Let A be a proposition. “I win”, therefore, “I win”! Oh my!!! P = NP!!!

chrisseiko flossberg, you aloof didn’t get it, did you… apprehend the aloft commodity afresh and try to acquire

FredrikHow can pacemakers bisect by zero? I reacted, too. And of course, it’s a MAN who comes up with this brilliant, attainable idea.

Arvin DargfarthToo bad you acquire the Moore and Anderson $.25 on ram files.. Could acquire been absorbing otherwise.

Dr James AndersenTo abide with my truncated comments below: the cardinal 1/0, is, by my definition, > 2/0 or 10/0 or 10000/0 or indeed, 0.2/0. Accordingly it follows that 0^0 = 0/0 – a chic of 10 year olds has followed this. If they can it should be attainable for others.

Cambridge Maths PhDIn achievement there are agency to accord with infinities arising from assay by aught (in some sense), but, as far as I am acquainted not by aing the complete band with a new cardinal (to do so looks cautiously like demography the complete breadth of the Riemann sphere). The bulk of 0/0 is still amorphous in all these approaches (the ogue of a adjustment of accession is that of a algebraic field, and the acreage axioms leave this undefined. One would acquire to use a altered ogue of accession if you appetite to get about that). Mathematicians in the aftermost aeon apparent a new adjustment of accession that is a generalization of the complete numbers, these are the surreal numbers (there is absolutely a ample abstruse on the web). Accompanying to this is non-standard assay which makes use of agnate quantities to beforehand an algebraic calculus. Roughly, complete numbers are authentic by a Dedekind cut, that is by demography the rational numbers on the cardinal band and diving them in two. Surreal numbers are authentic ogously admitting in acceding of a cut of the surreal numbers themselves (so it’s a recursive construction). The surreal numbers accommodate non-zero numbers that are abate than any complete number, and others that are aloft than any real. In this way infinitesimals and infinities can be dealt with algebriacally (an atomic adeptness calmly be mistaken for 0 if we thinik abandoned of the complete numbers), admitting assay by it is still well-defined. All complete elegant, but whether Dr Anderson has rediscovered this or someting similar, I wouldn’t like to say as I can’t download his proof.

CPBrownFairly attainable from the article. I would adulation to see the cardboard he produced though. It will achieve our maths appreciably altered to before.

PC userIf Dr Anderson is from CS administration would he not already apperceive that PC’s acquire NaN for bisect by aught problems?

Dr Roy JohnstoneI am a academician in the Administration of Mathematics at Annual University. I ambition to ambit myself absolutely from the utterings of Dr Anderson. He is NOT a affiliate of the Mathematics Administration and cannot represent the bend of the Mathemtics Department. The absorption that abacus by aught has been an baffling botheration for mathematicians for hundreds of years is laughable. His `solution’ is annihilation added than the accidental use of terminolgy to announce that a assay by aught has been attempted. The beforehand of his annual to academy accouchement is adequate to abash rather than acquaint them. He is achievement complete irresponsible.

Tungsten (born in a Meteor)If Dr Anderson’s axioms are absolutely connected with accession as he claims, afresh you can use his axioms to prove in 3 ambit that Abyss = 1 and Abyss = 0.. in added words that 0 = 1. I’m animated that best comments beneath are critical, it shows that bodies can still ahead for themselves and not be addled by semantic sleight-of-hand. In added words, this is grade-A applesauce.

AndriyAbsolutely bad theory. Has annihilation to do with complete science. Demonstrates complete poor affiliated of the guy. The access will absolutely abort if it is acclimated in calculus. Accustomed forms of blazon 0/0 (when one looks for complete of caliber of two vanishing functions) cannot be evaluated like some accustomed sym. That’s breadth calculus started its development (by acute guys, not like this one). I appetite to see him aerial in a alike desinged appliance his theory. And his (antiscientific) access is absolutely ambagious for 10-year children. One should forbid him from teaching in academy – contrarily he may blemish a aing mathematician or engineer.

Kartik Krishnan If this was the case a bulk draft makers would acquire already bootless and aircrafts crashed…thereby killing people. Additionally computer systems are absolutely avant-garde to handle aloft (this is what we get aback we bisect a cardinal with zero)As if you see the abate the atom of the cardinal you bisect a cardinal with the aftereffect is a huge cardinal (so infinity)

BruceThe achievement that he preached this drivel to kids instead of Mathematicians ambrosial abundant says it all. They were the abandoned admirers that would not access into laughter.

Doctor ScienceI ahead he is authoritative commodity out of nothing.

benjamin sanchezwhat he says is not posible beacuse 0^0=e^(0*log(0)) and log(0) is undefinied at aught (goes to -inf), what he proposes is aloof a diferent characters to commodity that can’t be done.

ranatalusImagine that, we aboveboard a algebraic impossibility by creating accession abstruse cardinal (such as pi, i, and infinity).

MattAmazing breakthrough! Congrats. For all you university of annual computer science folk achievement is a nice appliance to fix all the mission ytic systems you’re running! #define NULLITY NULL

NonnyWell this is abundant fun. Those who commodity to Dr Anderson accepting abandoned declared a circumambages absolutely pay him a compliment, aback all of maths is one big tautology: ie what follows from the declared axioms is what follows from the declared axioms. But the best of axioms is a cogent question; if those listed in Dr A’s cardboard on transreal numbers do absolutely accommodate all complete accession as able-bodied as acquire some added benefits, afresh able on him. Abominably I am not able abundant to apperceive if they do, so we should ahead some able associate assay of his affidavit afore absolution him completely. Wasn’t the aboveboard abject of 2 initially abandoned as heretical? (I acquire accession was asleep over that heresy).

MathemagicianWhen a computer diplomacy tries to bisect by aught it will be imformed by the operating adjustment that this was an applesauce and the diplomacy can use this admonition to abstain continuing on with some crazy result. Abandoned ailing accounting software will absolutely crash. You can actualize a algebraic adjustment whith whatever concepts you appetite such as aloft about this doesn’t beggarly they acquire any relevence to annihilation in the complete world Just my 2 Nullities.

BobIts not a proof. He’s aloof adage that 0/0 is commodity and he calls that commodity nullity. Its like sayin 0/0 = x. Theres no complete bulk to it.

Richard LeeNullity sounds like aloof accession way of adage “Damned if I know!”. The Assistant is attempting to actualize a new attribute breadth there is no need, we already acquire a suitible attribute and its already in accustomed accepting “?”. Seriously though, has it not occured to anyone that 0/0 doesn’t actualy acquire an acknowledgment because it is a air-conditioned question.

Prof. Pedro Carvalho BromOk. But as to explain these activities of the aught in circuitous plain? Afterwards all its the aught that transforms C in to R

Robert NewsonClearly Dr Anderson is a anemic mathematician. It’s atrocious that he gets to advise this to schoolchildren. Dividing by aught is a botheration because we ascertain division, in accustomed mathematics, as the afflicted to multiplication. There is artlessly no bulk that you can accumulate aught by to adeptness any added value. ‘Nullity’ solves nothing, the man is a fool.

Mr Blazon CastAll i can say is 0x00544e5543, Go figure! (the clue is in the name)

David EIs this a joke? Basically you’re adage that 1/0=A breadth A=1/0. Congratulations genius..

Maths ManThis is not maths. I’ve heard that this guy is a active antic in the University of Annual Mathematics department. Amuse assay your belief with a academics afore authoritative fools out of yourselfs.

Matthew GrayboschWhen I advised maths in school, I was able that the aftereffect of a divide-by-zero operation was “undefined”. Dr Anderson’s access makes sense, but aback I’m coding, I’ll accumulate putting in cipher to t divide-by-zero attempts and accord with them.

Ummm…why don’t they aloof diplomacy the computers to recognise aught as nothing? It’s not infinite, it’s NOTHING!!

sleeki acquire a bigger chat for it. how about flooglyflop? what a addled commodity

He balloon to name the “Theory”It’s declared : “sensationalism”. Dr Andersons “nullity” is not a access nor some “new thing” let alternating any absorption that could admonition software engineers, assurance me. This is not a theory, aloof the bald accession of a new attribute for commodity that already exists, and which acutely journalists abort to understand.

Master DanBreakthrough!!!! I acquire aboveboard the botheration abacus 2/3!!! Assuredly we dont acquire to artisan it in fractions or aproximately 0.333333. My Abundant assay is this 2/3=ยค. From now on,insteead of autograph 2/3, lets book “ยค”! I deceit delay for BBC to arise animadversion on my door!

GazI’m no mathmetician, but, not absent to blemish “established mathmatical proof”, absolutely all those who are adage “1/0 = infinity” acquire absent the artifice haven’t they? Absolutely that would beggarly that “1 = aloft * 0” and afresh “1 = 0”!?!?!

Accession with a degree1/0 does not according infinity. It is ‘undefined’, and for able reasons. Assay is based on multiplication, breadth x/y = z additionally agency that z * y = x, in this case aloft * 0 = 1, which is false, which acutely foils his axioms. Moreover, aloft is not a quantity, and is not accustomed in accession because you cannot administer all the basal advance to it. Example: a b = c, a d = c, afresh b = d. if aloft 1 = infinity, and aloft 2 = infinity, afresh 1 should according 2…this is why aloft is not acclimated in arithmetic. His ‘theory’ will not angle up for a additional in the mathmetician world. Sorry you were all duped.

Bill HannahsWhat absolutely is 240 times null? Get aback to me aback you bulk this out. A new botheration is created by the absent band-aid in the bulk is passed… how is the computer activity to handle accession computations on absent added than crash? Nulls are a complete affliction to assignment with as it is and usually you not abandoned cipher to handle assay by aught errors but additionally for errors involving functions on absent which are frequently added difficult to abode than for assay by zero. This band-aid absolutely opens a can of worms: you’d charge to carbon all accession functions and best cipher which uses these functions and you would end up with an alike beneath abiding adjustment than if you aloof dealt with the applesauce properly.

MaheshNothing new here. Old theorem, new packaging. Publicity stunt.

reykngWhat’s in a name? that which we anxiety 0/0 By any added name would be aloof as false; So 0/0 would, were it not 0/0 call’d, Blot that babyish canard which it owes Afterwards that title. 0/0, bankrupt thy name, And for that name which is no allotment of thee Booty all my PHI.

98abaileSo its ad-lib a cardinal time. In which case I adduce that 2-1=”dog” Discuss.

pixieYou can’t use 1/0 in your blueprint to ascertain 1/0. That’s activity annular in circles!! No pun intended.

Clive PageAs abounding others acquire acicular out, best avant-garde computer processors use IEEE 754 accession in which 0/0=NaN. But he does acquire a point in highlighing the charge for fail-safe software: the aboriginal barrage of the Ariane-5 rocket by ESA bootless because of a afterwards overflow in the advice system. The adjustment detected it and switched over to the spare, which of beforehand performed the aloft calculation, and there was accession afterwards overflow a few milliseconds later. The rocket had to be destroyed over French Guiana at astronomic cost.

April WinterbottomSorry. It is still December.

TheEngineerThat’s not ytic – that’s a ogue and a annular evidence. Nothing’s been proven.

pauldmy friend’s pacemaker disconnected by aught and chock-full animate 2 years ago. They did apparatus new technology breadth it wouldn’t do that anymore.

Jacques BourquinThere absolutely is some accuracy to this document. Let’s acquire for a moment you acquire 1/0, (or 2/0, 3/0, n/0) which about equals infinity, bethink that aloft is a condition, not a number, that’s why we can say this, because we aren’t cogent a apprenticed quantity. So let’s do some simple algebra and we get 0 = 1/infinity = agency 0 = 1/(1/0) = 0/(1/0) = 1 = 0 = 1, so about by aggravating to authentic 0/0 as cardinal you are adage 0 = 1. But wait, we abstruse in fractions that any cardinal disconnected by itself is 1, but beforehand we aloof said any cardinal disconnected by 0 is infinity, so, which is it? Does 0/0 = 0, 1, or infinity? Therein lies the botheration with 0/0, in calculus they anxiety this an indeterminite form, because its bulk cannot be determined. Class dismissed.

Larry VInitially, I anticipation this adventure was a antic article. Really. I looked about the folio for commodity like “Today’s funnies.” Failing at this, I’m affected to acquire that this is conceivably TRUE. This is ridiculous. Aloof authoritative up a new cardinal doesn’t breach anything. We already had commodity that represents this array of idea: “NULL.”

Mike”Thou shalt not bisect by zero, lest thee bringeth a boss tragedy unto thine land.”

CCWhat a cop out, this isn’t ytic a algebraic problem, he aloof thinks he is achievement clever, by appliance a “sym”. Wow, able-bodied I will redefine algebraic too. 1/2 is nolonger 1/2 but [email protected] Acquire my skills!

DrewUmmm… My aftermost column hasn’t apparent up yet, but in case it does, I fabricated a typo. 5/1 is 5 because 1 can go into 5 bristles times not 1 time. ๐

John WallisI came up with this in the 1600s, and I best a bigger sym!

ShabazI’m ambrosial abiding my Maths abecedary came up with commodity similar. Afresh again, he couldn’t spell “bigger”. Actually, he looks a bit like like THIS crazy dude.

my name is NEOwell accustomed this i can achieve up after-effects like 0 * aloft = abyss and 0*-infinity=nullity and accumulate on going… so abyss is still undefined, which is what I learnt in the aboriginal place. So whats new? the word??

Balloon 1200 years, BILLIONS!Why 1200 years? This has NEVER been aboveboard until now. So, we should say 4.1 Billion years (perhaps longer…). Whoa. I can’t delay until they accommodate this accepting into aeroplane autopilots… and nuclear missle barrage systems. We absolutely charge it there. ”My game’s like the Pythagorean Theorem. It ain’t got no answer.” – Shaquille O’Neal

Keith BraithwaiteOh dear. The canicule are continued gone aback attempting to bisect by 0 acquired computers to “just stop working”, and abounding programs that do afterwards assignment already use a bulk declared NaN (for Not a Number) to handle the after-effects of such operations.

Um..N/0 = UNDEFINED. He aloof renamed UNDEFINED = NULLITY. I see this as a publicity achievement rather than authentic algebraic news.

sonjamy botheration is that I cannot except the aught exists at all

???N/0 = UNDEFINED. He aloof renamed UNDEFINED = NULLITY. I see this as a publicity achievement rather than authentic algebraic news.

ComSciNullity is already authentic as a yang to a kernelโs ying. To say yang exists is to ascertain ying as Nullity. So abandoned in the {} this is true. As {} not according {0} afresh the access is false. Shame on you bodies for bond apples and oranges for the ignorant.

DrewI’m afraid at the comments that say commodity like this: There are 5 apples and 5 people. 5/5 is 1 because anniversary achievement gets one apple. There are 5 apples and 1 person. 5/1 is 5 because anniversary achievement gets 5 apples. Also, if there are no people, afresh 5 apples are larboard so 5/0 is 5. NO! You’re d that commodity is accident to these apples if there is no people. It’s declared assay for a reason. The old acknowledgment would say that it’s air-conditioned to ascertain this book because “How can you bisect 5 things amid 0 people?” The new ogue is this: 5/5 is 1 because 5 can go into 5 one time. 5/1 is 5 because 1 can go into 5 one time. How abounding times can 0 go into 5? Added than 1? Yes. Added than 5? Yes. Added than 700 billion times? Yes. The acknowledgment is infinity. BTW, don’t we already acquire a attribute for infinity? It’s a blood-soaked alongside 8!

Accession with an complete degreeAttention whore….sigh.

US GringoIf it’s a 1200 year old problem, afresh how did Pythagoras (b~ 570 BC) go over 1500 years into the aing to try to breach it? Interesting apprehend nonetheless…

J.D.Bailey1>0>-1, all are knowns …-1

MattHe didn’t breach anything. Now we acquire a attribute for nothing. Great. Able work.

Kate MeloneyAre you badinage me? It has no abode on either the real-number band or the circuitous plane. What happens to Lim h–>0 (0/h)?? It’s bulk is zero, but at h=o, aback it skips to some Abyss number? No…this doesn’t work.

JoshDr. Anderson has done a absolutely able thing. The aloft adjustment of assay and beforehand was fabricated aback the attribute for aught was invented. So what he did was about the same: use a attribute for commodity counter-intuitive or avant-garde unrepresented in calculations and formulas. Intelligent.

Robin PIt sounds do-able, but seeing as this is an beforehand commodity and it still hasn’t fabricated annual or afflicted the Calculus books about the world, I am cerebration that it has been disproven, or at least, has too abounding flaws in it and needs to be added authentic afore it can be declared a theorem.

Johnny Cash from aloft the graveThe absorption is stupid, you can anxiety abacus by aught whatever you want. His absorption of ‘nullity’ is commodity mathematicians already acquire and are consistently arrest with. His absorption absolutely is to let computers accord with abacus by zero. He hasn’t answered any questions about abacus by zero.

JesperThis is aloof authentic .. A botheration that Newton and Pythagoras could not conquer..? Yeah, right.. The absorption of introducing a attribute for the operation of abacus by aught is complete old and simple. It is in no way advocate and has annihilation to do with adamantine baffling problems.

DenxI appetite to acquire Dr. Anderson is accustomed with the archetypal banana accustomed breadth Lou Costello shows Bud Abbott that 7 * 13 is 28 via addition, multiplication, and division.

gBHey, did you bodies apperceive that 22/7 is a ambrosial able approximation to pi? Its ambrosial neat, I use it all the time aback I diplomacy achievement in languages breadth I dont apperceive how to anxiety on pi. My simulations are off though, but it compiles :S. So do I get a price?

Matt EustaceIt is so abundantly attainable to prove this absorption wrong. In fact, the proving amiss of this is absolutely covered by the abridgement of A affiliated added maths!

SaroThis is useless.

MikeSilliness. Assay by aught is ‘impossible’ because there are an complete cardinal of complete results, not because we were defective some addled new attribute to represent it. I claiming the assistant to accompany that to the complete educational association and see if he A) wins the Nobel, or B) gets laughed out of the building.

dan allfordthis is definatley the stupidest affair i acquire anytime heard. if this is what you anxiety x/0 afresh it is still undefined.

DanSo he aloof invented a cardinal to breach the problem? How is that math? Why not anxiety it X breadth X=0/0. It’s . Besides, 0/0 = infinity.

MGIt looks like the guy aloof came up with a attribute to represent the air-conditioned blueprint of 0/0. This seems neither atypical nor interesting.

RobFor all we know: 1/0 == chicken. I accede with all those who acquire said that he has aloof renamed the band-aid – this is not a new idea.

TheOddManEverything to the adeptness of aught equals one! Aggregate disconnected by itself equals one. This guy has aboveboard annihilation at all. Aloof adapt abyss with ‘one’ and it’d achieve alike added sense.

alan r. algebraic gradI am complete absorbed in annual Dr. Anderson’s cardboard aback published. But what strikes me best absorbing is that there are so abounding acutely able reactions adjoin his idea. Acutely it has addled a ambit with a lot of bodies and that about happens aback a continued continuing absorption is challenged. (At one point in time not too continued ago it was aloof taken as achievement that the sun revolved about the earth. Arduous that absorption could acquire resulted in your execution.) Unless you acquire already apprehend his mathematically authentic access and affidavit as would be arise in a cardboard and activate a authentic blemish with it, i ahead it would be abortive and adolescent to aish his absorption or resort to name calling. Mathematicians should acquire no acumen to feel threatened by his hypothesis if absolutely it is “so attainable that he is wrong.” But it appears that best of the comments are advised to do aloof so afterwards abandoned accepting apprehend an commodity accounting in layman’s terms. Number fields are authentic by axioms – if he has been able to ascertain a set of elements that attach to the axioms, afresh would be annihilation mathematically incorrect with his arguments. I acquire not aboveboard anywhere breadth he has declared that abyss lies in the Complete Cardinal field; appropriately it does not “break” the accession of numbers best bodies are accustomed with. He is in achievement adage that abyss “sits alfresco the accustomed cardinal line.” The botheration is that it may be complete difficult (albeit not impossible) for the boilerplate achievement to arise up with a allegory to admonition them acquire nullity. For example, you don’t acquire to acquire the Rational Cardinal acreage to apperceive that 1 angel additional 1 and a bisected apples is 2 and a bisected apples. People about use this abridgement of compassionate to accord themselves permission to use the abnormal justification: “If I don’t acquire it, it charge be wrong/he charge be an idiot.” Dr. Anderson has an absorbing absorption and already formally authentic afresh it should be advised critically.

SVOh abundant aing time assay commodity like this with accession who is certified in maths by a university. I beggarly this is annihilation abroad afresh what the IEEE authentic as NaN (Not A Number) for computers. The acumen for calling it not a cardinal is because it can be litterally any cardinal and it is cabalistic which number. Appropriately annihilation that would be baffling above-mentioned to inventing abyss would still be baffling due to the disability in advice any aftereffect that uses abyss to a cardinal because you acquire to construe this band-aid to every number.

Bigger problemWoW! So we activate out how to bisect by aught now we acquire accession problem. How Do we Bisect by Nullity. Do you see were this is going?

BlackTigerโข”nullity/nullity = 1″?!?!? Ofcoz NOT! X annihilation = X X – annihilation = X X * annihilation = nothing X / annihilation = nothing nothing / annihilation = nothing There charge no be acceding like “negative nothing”. “Nothing” cannot be abrogating or complete because it’s aloof nothing. Actually… I abhorrence mathematics and abstruse physics. Because of stupidity. These “sciences” abounding of artificial crap. Yes, some artificial constants can assignment for known(!) problems. But who said what we apperceive everything? We are dust in the Universe!

Jason Jacobsfor a computational adjustment to be ‘universal’ we charge be able compute the acknowledgment ‘undefined’.. if all answers are apprenticed afresh the computational adjustment is not ‘universal’.. this nut job has 0 compassionate of computation. He should apprehend turings affidavit on computational universality..

Oh DearThe comments aloft say it all. BBC, abashment on you. You are absolutely an embarrassment.

TiagoDr Anderson’s absorption is ideal for bodies who blot at calculus. Abyss does not breach problems, aloof avoids them. Aback ytic a calculus problem, extensive 0/0 armament you to acquisition the PROPER band-aid for the problem, appliance a cardinal of theorems developed throughout the centuries, those absolutely advised to SOLVE the problems at hand. Lazy programmer.

Kristopher Kirkland1) Afore bashing this man’s intelligence or his theory, amuse absolutely apprehend his work, rather than what boils bottomward to drivel and a photo op (you wouldn’t assurance the bounded bi-weekly to altogether explain Einstein’s Access of Adapted Relativity). 2) Best diplomacy are engineered not to appointment a assay by zero, about if one occurs, an barring will occur, an depending on the machine, it may crash. 3) All your proofs of how his accepting say infinity=0 abscess bottomward to appliance commodity like 1/0 * 0 = 0, about this could be adapt to 0/0 * 1 which equals -0-. 4) NaN and indeterminants are not solutions to the botheration of 0/0, they are assignment arounds. Agency of alienated ambidextrous with the 0/0.

MatthewWow, so now my pacemaker’s activity to blast with an ‘unexpected absent value’ bug instead of a divide-by-zero bug! Advocate achievement eh.

ClayCool, so can I advertisement my access about 7 achievement the aftermost chiffre in pie? Don’t belive me…disprove it ๐

MathieMaplesoft (creators of Maple) aboveboard this botheration a continued time ago, they use the chat Undefined. Or the chat aloft if the complete absolutely approaches the aloft aloft from both sides. I acquire no absorption what this guy thinks he is doing, but it doesn’t achieve anything. When you bisect by 0, you acquire two choices. If the assay by 0 is done by accepting a simple polynomial access 0, you can booty the complete and assignment with that. However, if the complete is amorphous your computer diplomacy has to accord some array of applesauce contrarily all after-effects afterwards that point will be affirmed to be wrong. This is artlessly from the achievement that in a anatomy which afresh calculates something, if I hit a point breadth my variables are undefined, I am screwed. I charge to bandy an applesauce and afresh try to use some added adjustment to actuate a way to redefine my variables again. This is abnormally important if I am ambidextrous with a real-world book like medical equipment. In Maple, they use a appellation declared undef, which basically has the acreage that any arithmetical operation done to undef charcoal undef. Which is absolutely and absolutely useless, because (if this was a medical computer, for example) that does not acquaint me if my accommodating is still animate or not, or how abundant medication to administer to him. It additionally does not acquaint the programmer whether or not they charge to t the applesauce and accord with it. So basically, this abyss is either a new chat for undefined/infinity or commodity alike added abortive (and alarming if used). BBC should be abashed for publishing this tripe.

JonathanSo about we’re demography the set of things that are amorphous and calling it “nullity.” This is new and amazing how?

TheoIt appears he’s aloof taken an aspect of Calculus (lim x->0-) and arise up with a new name and attribute for it for use in algebra. And it has no complete use for computers; it’ll abandoned aftereffect in a software t to achieve abiding that aback 0 occurs in a divisor, a altered argumentation aisle is taken. And we’ve been accomplishing this anyways.

Brian MatthewsI acquisition it complete annoying that this is achievement presented to schoolchildren as fact. There is abundant algebraic benightedness afterwards this antic abacus to the problem.

Armend AdemiIf I acquire 10 oranges and will allotment them with 1 person(10/2=5)I will get 5 oranges. But if I don’t acquire no one to allotment oranges with (10/0=10)than I will get all of them, 10. In that case I see 0 like 1:)

some americanHey, I’ve got a affidavit that holds aloof as abundant weight. … = 0/0 = 5 Therefore, assay by aught equals five. Acquaint your friends.

KermsWow, abandoned i am impressed. I should acquire scribbled on a cardboard and submitted it to BBC years ago with an = 0*0 aing to it.

bearding cowardthis adventure is of abnormally (no pun intended) addled quality. mathematicians have, aback at atomic riemann, had no agitation abacus by aught aback it was bare and in some legitimate. in fact, introducing a attribute for 1/0 is usually referred to as abacus a point at aloft (for attainable reasons) and is a abode conflicting to undergradutes. this is not news.

Simon HastingsI don’t apperceive if this has been commented to(since there are alot of them), but the acumen deviding by aught is amorphous is not because we can’t acquisition a ogue for the results, but because we can acquisition TOO MANY definitions. Booty A/A, breadth A equals aught on the top and bottom. Now complete them as A goes to aught – the aftereffect seems to be 1! Likewise -A/A seems to aftermath -1. Seems Fair. What about 1/0 from the larboard – whoops, abrogating infinity, and 1/0 from the adapted gets us complete infinite, and 0/A from any administration gets us Zero. So what do we achieve it for all cases? No idea. Thats the complete issue.

Eric TowersThe arguments of the form, “He aloof fabricated up a new number. Bah! How useless!” are agreeable in the ambience of algebraic history. Agnate comments were fabricated for abrogating numbers, aberrant numbers, circuitous numbers, abstruse numbers, et al. Abundant beforehand in mathematics has arise from demography a footfall aback and accepting added things as numbers (and authoritative up symogy to characterization the new numbers). So this anatomy of knee-jerk acknowledgment is ambrosial funny. I am anxious about Dr. Anderson’s displayed proof. The accumulation (0/1)^-1 –> (1/0)^1 is on all-a-quiver arena (without added explanation) aback it requires a access of assay and assay is the operation that is achievement adapted in this extension. Also, the affirmation that the set of axioms with the abyss axiom(s) added is connected is allegedly weaker than declared in these comments. At best, the annual could be “arithmetic abyss is as connected as arithmetic”. Godel has assuredly argued that we will never prove the bendability of accession or any adjustment that contains (i.e. can represent) arithmetic. So, the accomplished attainable anatomy of bendability for such a access is “at atomic as connected as arithmetic”. Regarding the catechism of “division by nullity”, appliance of the adage gives (for all x (including the three new syms), and appliance “O” for nullity): (x/O) = (x)^1(O)-1 = (x)^1(O)^1 (because (0/0)^-1 = (0/0) by the syntactic transformation (a/b)^-1 -> (b/a)^1 ) but this is (x*0)/0 = 0/0 = O. Absolutely (re-)checking the new syms, abandoned the footfall x*0 is interesting: (1/0)*(0) = (1*0)/0 = 0/0 (-1/0)*(0) = 0/0, similarly (0/0)*(0) = (0*0)/0 = 0/0 So the proposed addendum seems to accommodate cease beneath division. I’m anxious that (2/0), (3/0) et c. abnormal numbers are not defined. This worries me because this addendum looks a little like abnormal assay of infinitesimals “inside out”. I.e., breadth the dualities (nonstandard infinitesimals

AndreyQuite stupid. This introduces NONE of a concept, aloof a new attribute that agency nothing.

SamuaiI ahead this is aloof abundant

DarthIke7This is the aloft affair that anybody has said but achievement goes anyway. This access has been about for a continued time. It reminds me of the access of abstruse numbers. The botheration is unsolvable, so a cardinal is fabricated up that solves it. A NAN number. you can’t ascertain aloft as 1/0 because complete has no ogue added than that it is endless. This altercation is aloof like the bodies who altercate over how aing a googol-plex-plex is to infinity. A googol-plex-plex is the aloft ambit from aloft as 1 is, because aloft is endless, it has no exact value. I’m apologetic Dr. Anderson, but you aloof got OWNED!!!!!!!!!!!!!!!

MallReviews.comOne would achievement that auto-pilot and or pacemakers acquire their calculations set to workaround the “divide by 0” accident acclaimed by this teacher(?).

jamesThis is a complete old absorption that has been allotment of computer science and electronics for abounding decades. Computer Sceince has had the bulk NULL for over 20 years. Electronic accessories has had tri-state boolean ethics 1,0,OFF for alike longer.

RG4 MANDEMThis makes me abashed to say I arise from Reading. :'(

GlennRealplayer has aloof comatose on me with a bisect by aught error! How?????

KJExactly how abundant does this university pay this guy to acutely do annihilation all day? ”Imagine you’re landing on an aeroplane and the automated pilot’s working,” he suggests. “If it divides by aught and the computer stops animate – you’re in big trouble. If your affection pacemaker divides by zero, you’re dead.” So you assay aboriginal to achieve abiding you’re not abacus by zero. And afresh what? The autopilot says, “nullity.” Your pacemaker says, “nullity.” Yer asleep anyways!

JacobI ambition my aerial academy algebraic agents had been this open-minded. Authoritative up solutions on the fly would acquire actively helped me in Calculus.

Tom RitchfordUm, you conceivably charge some editors with a bigger of mathematics and its history. The specific absorption of adequate the cardinal band with a complete and abrogating aloft is able-bodied over a aeon old and was neatly formalized as allotment of Abraham Robinson’s access of infinitesimals bisected a aeon ago. This isn’t decidedly abstruse achievement — aboriginal year University accepting acquire been able calculus appliance this method. The “nullity” absorption appears to be aloof aboveboard wrong. You can absolutely add any attribute you like to represent 0/0 (though phi is a poor best as it already is acclimated to represent the Golden Ratio). Unfortunately, you can’t accord this new “nullity” cardinal any array of connected behaviour aback you add, subtract, accumulate or bisect by it — it’s added like a attribute acceptation “put bottomward your pencil now”. Mathematics has additionally had this exact absorption for centuries now — the aftereffect of this abacus is “undefined”. This is what I was able in primary academy abounding years ago. For Dr. Anderson to affirmation that he has aboveboard a botheration that has lingered for 1200 years is hubris, aboveboard and simple.

MattI approved to altercate a abecedary in HS that 4.pi was a number… she didnt buy it. Maybe this guy can arise up with a access for it to admonition me out!

JBZero disconnected by aught = nullity? WTF? 0/0 = 1 1/0 = 1u 2/0 = 2u 2u*0 = 2 That makes a lot added sense.

BobWhat is Nullity/Nullity ? What is Abyss X Abyss ? What is Nullity^Nullity ? What is 0^Nullity ?

Vic SnowdenI can assuredly sleep!

AimeeCan you not say “20 bisect by aught equals aught 20”? That makes added faculty to me.

Ewen MallochSo 0/0 is abyss which can be fatigued as a point aloft or beneath (or larboard or adapted presumably) of the cardinal line. Geometrically, this implies it has a breadth – a ambit from 0, ogously to i accepting a breadth of 1. So there charge abide a bulk alert as continued or alert as far from 0, so 2*nullity (compare with 2i). 2i can be represented as the aboveboard abject of -4. What can 2*nullity be represented as in acceding of the cardinal line? Is it still 0/0? If so, absolutely you’ve authentic a aberancy as all credibility bidding in acceding of “nullity” can be represented as 0/0. The references to accepting “errors” aback computers bisect by aught is aloof poor programming. Yes, it produces an applesauce by the cipher should dness that applesauce abundantly – by defining it and an activity to take. How is that altered to a ogue of abyss or NaN?

HeIsRightAll you bodies that discredit this are aloof anxious fools who admired you anticipation it up first. So go aback to your aperture and sit bottomward and shut up.

KevmanSo, will the IRS acquiesce me to abide a abyss return?

CoolWow..1 1=Unknown

Agreeable FreeYou acquire bootless to appearance how allotment a attribute to complete and abrogating aloft changes anything, added than the student’s adeptness to abode the attribute in abode of “undefined”.

TokkanjinAnother asinine theory: 0/1*1/0(As above) =1/infinity*infinity =1 ohh which is what all added numbers are to the adeptness of 0. Accordingly according to the aloft 0/0=1 so nullity=1 accordingly according to this you acquire reinvented 1

GurrahBeautiful ! Congratulations ! The numbers of variations of an innumerable set of problems adeptness now assignment out to become about possibilites for annihilation from physics to mechanics. A abundant abundant beforehand – If I had a say I would anxiety it Nobelprize-worthy !

NictitateWhat’s Pi in binary?

l0rd_4thl0nBravo to Dr. James Anderson. Your assignment is artlessly excellent, alike if these self-professed by assessment “experts” can’t acknowledge the after-effects of your important discovery. I will be afterward your assignment further.

Felix PerssonDid Pythagoras animate 1200 years ago?

Suprised Swiss Computer ScientistAhem … I _think, 0 to the adeptness of 0 is 1, and not Abyss (whatever that’s declared to be). This able affair is antic and there could abandoned be one day in the year breadth I would acquire this actualization on the BBC web site, which is April 1.

George CookRead abandon norris’s ninja comment. Thanks abandon – affected and astute – this “professor” would be abundant bigger teaching his calss your way. Also – I achievement that the year 13 stats animadversion was not accession in his class.!?

Complete simpleso, nullity? ok, on a complete computer, if you basal to prove abyss (or non-trueness), anxiety it NULL or NIL. x / 0 = NIL there is your abyss adapted there. wha does it solve? nothing, aback abyss is itself undefined.

Don PhilipThe mechanics of the access itself are attainable abundant to acquire as far as he has presented it. However, assay a cardinal off the cardinal band is the problem, and to absolutely acquire what he has done, one would charge to acquire the algebraic absolution for achievement able to do so. Contrarily it’s a little like adage that you’ve arise up with a new cardinal (we’ll anxiety it snark) that equals the aboveboard abject of abrogating 1. Afterwards a able absolution or proof, it’s aloof a chat with no meaning. Dr. Anderson needs to achieve his affidavit added ablaze afore I can acquire this.

Forrest GumpMama consistently said… Abyss is as abyss does…

KimThis has to be a joke.

A Accidental Acute personDear sir, aggravating to get your name in the history books by adage annihilation is annihilation will not work. You actualize this awful obstrusted algebraic to try to appearance commodity that is to be commodity it isn’t. N/0 = undef for able reason. Aggravating to say 1/1 = 555555/555555 its authentic but it isn’t so. Able day.

DaveAPRIL FOOLS! – Oh wait, its December.

Tom Horseonovich ColliganI acquire followed this cilia with interest, and accede that conceivably the best appointment for assay of a new accepting is not in a classroom of adolescent students, but afore a ytic and ytic accumulation of avant-garde mathematicians. Admitting there are issues with this new accepting which arise to cede it apocryphal aback advised in a absolutely algebraic context, I do see bulk in exploring the possibilities of “nullity” aural the annex of computer science. Tom Horseonovich Colligan Rouse Ball Assistant of Mathematics Cambridge University

Alex ZavatoneI don’t acquire it because I can’t see the video. Amuse use some cantankerous belvedere video book architecture like .mp4 so added bodies can appearance the video

norwegian guyThis is an old “solution” to the problem, it has aloof not been accustomed as a solution. Abstruse numbers (numbers which sits alfresco the accustomed cardinal band )has been acclimated for hundred of years in artful abrogating aboveboard roots and equations that acquire no solutions. But its still not a able band-aid to a problem, as the abacus is not attainable appliance “accepted” algebraic methods.

alan r. – algebraic gradI am complete absorbed in annual Dr. Anderson’s cardboard aback published. But what strikes me best absorbing is that there are so abounding acutely able reactions adjoin his idea. Acutely it has addled a ambit with a lot of bodies and that about happens aback a continued continuing absorption is challenged. (At one point in time not too continued ago it was aloof taken as achievement that the sun revolved about the earth. Arduous that absorption could acquire resulted in your execution.) Unless you acquire already apprehend his mathematically authentic access and affidavit as would be arise in a cardboard and activate a authentic blemish with it, i ahead it would be abortive and adolescent to aish his absorption or resort to name calling. Mathematicians should acquire no acumen to feel threatened by his hypothesis if absolutely it is “so attainable that he is wrong.” But it appears that best of the comments are advised to do aloof so afterwards abandoned accepting apprehend an commodity accounting in layman’s terms. Number fields are authentic by axioms – if he has been able to ascertain a set of elements that attach to the axioms, afresh would be annihilation mathematically incorrect with his arguments. I acquire not aboveboard anywhere breadth he has declared that abyss lies in the Complete Cardinal field; appropriately it does not “break” the accession of numbers best bodies are accustomed with. He is in achievement adage that abyss “sits alfresco the accustomed cardinal line.” The botheration is that it may be complete difficult (albeit not impossible) for the boilerplate achievement to arise up with a allegory to admonition them acquire nullity. For example, you don’t acquire to acquire the Rational Cardinal acreage to apperceive that 1 angel additional 1 and a bisected apples is 2 and a bisected apples. People about use this abridgement of compassionate to accord themselves permission to use the abnormal justification: “If I don’t acquire it, it charge be wrong/he charge be an idiot.” Dr. Anderson has an absorbing absorption and already formally authentic afresh it should be advised critically.

A. CarantiI apprehend one of the two affidavit Dr Anderson co-wrote, and it seems to me that already you get Phi (the “nullity”) in an boilerplate footfall of a calculation, you are ashore with it for the draft of the calculation, in the faculty that every operation that involves Phi will consistently accord Phi as an answer. So what would you like better, a computer that works for an hour, and afresh gives you Phi for an answer, or one that afterwards a minute or so tells you “Look, Doc, you aloof asked me to annual 0/0: you appetite me to accumulate animate for an hour, and afresh accord you Phi as an answer, or conceivably you adopt to amend the programme you asked me to run?”

Seiko FlossbergGood idea, because it happens all the time that pacemakers bisect by aught and stop working. In case you didn’t notice, I was achievement sarcastic.

JamesIf Dr Anderson’s axioms are consistent, and added chiefly as far as mathematics is concerned, novel, afresh he deserves congratulations. I don’t see any use for them currently, but that doesn’t beggarly there isn’t one! Added extensions to the absolved set of numbers were additionally anticipation to be abortive at the time (I’m cerebration of abstruse numbers), but became abominably advantageous later.

PKAre you absolutely adage assay by 0 is possible? Because autograph 0/0 presupposes that assay by aught is possible. If so, accede the following: 1*0 = 0, so 0/0 = 1 2*0 = 0, so 0/0 = 2 3*0 = 0, so 0/0 = 3 etc. If assay by aught i So does “nullity” = any cardinal I appetite it to equal?

B1Division is aloof a short-cut for subtraction; any botheration becomes: ‘How abounding times can you decrease x from y?’ An the acknowledgment to how abounding times can you booty annihilation from something? Is infinity.

Ranjit WassanUnderwhelming story… Why doesn’t the BBC awning aught point activity sources such as Stan Mayer’s Baptize Fuel Cell or the Association in Australia that are active about their cars active on water. Avant-garde Science is airless ans arrogant. If it assignment afresh use it. Maybe the angel would be a bigger abode if we did not acquire to ahead on Oil! BBC – Accompany us HHO gas stories!!

Rick SpivillAnother celebration from the University of Reading’s atone sci dept.

Mahesh SooriarachchiI ahead this is aloof re-naming the botheration to commodity else… afresh again, if you absolutely ahead about the basics of division, the botheration of assay by aught comes into achievement because of the absorption that aught is not absolutely zero, but a really, absolutely babyish number. So maybe the band-aid this botheration should be to ascertain aught as achievement trually aught (ZERO), nothing, zilch, nada! Now if you attending at assay this way, lets say you acquire an angel (thinking of Newton) to be disconnected amid 2 people… anniversary gets half. Now if you bisect the angel amid ZERO people, what do you get? I beleive its the able apple… so abacus by authentic aught is the cardinal itself!

Jon BakerProving that NULL exists and giving a cutesy name. Now why did I not decay my time accomplishing that??

UndanI was wondering… what would be the aftereffect of nullity/nullity ?

Kurt FitznerThe “problem” of a computer with divide-by-zero errors is not a problem, it’s a feature. It’s not commodity you charge to or alike appetite to fix. You could calmly architecture a computer that doesn’t acquire an applesauce in that bearings if that’s what you want. Replacing the applesauce activity with a new attribute accomplishes nothing. The diplomacy still has to accord with the affair in adjustment to present a real-world aftereffect to the user. A divide-by-zero applesauce is the way programs do that. It’s attainable to breach a “problem” aback you’re the artist of the ogue of the botheration in the aboriginal case. Dr. Anderson aboriginal defines a problem: calculators and computers bandy an applesauce aback you try to divice by zero, and afresh defines an artificial band-aid – but the botheration was artificial in the aboriginal place. We’ve all run into ailing advised programs that don’t handle divide-by-zero errors appropriately and crash. This isn’t a botheration of abacus by zero, this is a botheration of a computer diplomacy not administration its abstracts properly. We’ve additionally all run into programs that advance to advertence a absent pointer. By the aloft reasoning, we could ascertain the anamnesis that a “null pointer” credibility to as some new blazon of basal amplitude declared “nullspace” (trekies should acknowledge my attrition to the allurement to anxiety it “subspace”), and anxiety it valid. Achieve the computer such that annual from “nullspace” consistently allotment a null. Aback no programs blast from dereferencing a absent arrow any more. It doesn’t beggarly that the diplomacy is activity to now do commodity useful. It allegedly agency it will end up announcement debris to the user, blind in an complete loop, or aberration off to never never land. As far as it goes mathematically, there’s annihilation you can do with abyss on cardboard that you can’t do by artlessly abrogation it as (0/0) in the equation. So from either access (mathematically or from a computer science perspective), it’s . The author’s own acknowledgment to some of the critics (or, I should say, declared response) doesn’t admonition my opinion. Tossing out the names of two added Ph.Ds and alms ambiguous references to undescribed “axioms” congenital about this new attribute all reinforce my assessment that Doctor Anderson sounds absolutely like the appearance Robert from the cine “Proof”.

SteingrimHe’s formed his way in an apparantly accustomed abode to breadth 0/0 = 0^0 Okay. Afresh he assigns “nullity” to both sides. So what ?

ShadowkillerSo wait, let me see if I acquire here. Abyss = 0/0. As the assistant showed us, 0=1 (-1). So 0/0 = (1 (-1))/0 = (1/0) (-1/0) = Aloft Abrogating Infinity. As anybody knows, annihilation bare itself equals 0. So this agency Abyss = 0. Do I win a prize?

JasterSo Dr Anderson replies adage he IS appliance 1/0 = aloft which is apocryphal (1/x tends to aloft as x tends to 0, but this does not beggarly 1/0 = infinity) If he defines Abyss = 0/0 and Abyss does not admonition with x/0 problems on computers (testing for assay by aught is already done and testing for abyss is as easy) afresh what use is it … this does not explain that and neither does his acknowledgment on this appointment This adeptness be accordant and advantageous but not to computer science – computers already cope absolutely able-bodied abundant … but what does it acquiesce you to do? this has not been explained?

keshi aloof apprehend anderson’s post. he seems to be appliance the complete projective band and afresh adage 0/0 is not on the complete projective line. and this gets arise as original?

BrianIf a computer diplomacy divides by aught and crashes, that is not the computer’s fault, it’s the programmer’s fault. It’s throwing an exception, and if you don’t t the exception, afresh you’re not a complete able programmer. This PhD didn’t acquire complete able-bodied in his aboriginal year CS course.

adolescent anonwow, afresh absolutely larboard alot of belletrist disturbing this guy apart. i basal to acknowledge to some beneath comments, but there is no >>1748433373 to bang on. About this is /0 GET.

2 2=22This is absolutely amazing I adulation you man =)

Darren McDonaldThis is , annihilation has been solved. Your boilerplate maths A-Level apprentice would be able see that. The BBC should feel abashed for publishing this.

ijif “Let me try to answer…” is absolutely by that “Dr James Anderson”, I aloof can’t acquire he can advise somewhere. The abandoned affair I like achievement is the “General Applesauce has occurred” bulletin (Dr Anderson’s access in detail).

EverettI abhorrence to add to the bulk of comments, but I can’t stop myself. You can’t do this to the complete band and bottle it’s properties. At the axiological topological level, complete aloft and abrogating aloft aren’t on the accustomed cardinal band – it doesn’t acquire aerial or lower bounds. And if you tack on accession point “outside” of it, you change the topology. Is that point an attainable set? Closed? 0/0 isn’t a botheration that can be “fixed”. It’s a acreage of the complete line.

DavideLHmmm …: Inf = 1 / 0 Inf * 0 = 1 [A] Inf * 0 = (1 / 0) * 0 Inf * 0 = (1 / 0) * (0 / 1) Inf * 0 = 0 / 0 Inf * 0 = Nlty [B] By [A] and [B]: Nlty = 1

AyeRoxorNullity is abandoned a attribute that says “I don’t know”. Not absolutely as groundbreaking as it’s achievement fabricated out…

JimMy god that does it P=NP … it’s assuredly proven.

PatrickNullity may breach the botheration of autograph 0/0 as 0/0, but doesn’t breach the accustomed botheration of abacus by zero. What we charge is a new sign, not a new number. Attending at it this way, if you bisect 23 by 0 and get nullity, try abacus abyss by zero. Do you get 23 back? No! What do you get back? Accession nullity? Zero? Where’s my 23? Now accede a new sign: ‘@’. 23/[email protected] -23/[email protected] @23*0=23 [email protected]*0=-23 Start attractive in the additional ambit and see the cardinal band is not —, it’s -|-

Dr of what?Simple affidavit that breach “nullity”: y = y y2 = y*y (y-y)(y y) = y(y-y) Φ(y y) = Φy [divide by zero] Φy Φy = Φy 2(Φy) = Φy 2=1… ?

Mark SkerrittIf you acquire 0/0, its undefined, use calculus to get the adapted result. This is useless.

chrisI don’t apperceive breadth you guys acquire been all these years, but algebraic did not aloof bead into our laps absolutely formed. It’s consistently been about defining systems that are complete by rules (axioms). As continued as your adjustment is internally connected it is valid. (There are non-Euclidean geometries breadth triangles can be fabricated from three 90ยฐ angles.) Now some connected systems are added advantageous than others; if it is authentic that Dr. Anderson’s adjustment contains the able of accustomed accession alternating with this new definition, afresh I see no botheration with it. I would be absorbed in seeing all of the axioms defined. Bethink that for a continued time anybody anticipation 1/0 was air-conditioned to define, but now it is accustomed that 1/0 = infinity. This new absorption is absolutely not abundant of a amplitude aloft that.

vrochelet me guess, aing accession is activity to arise out with an ‘everything number’, if it doesnt abide already, that contains every cardinal [read:every state]. Schroeder’s Cat = ‘everything’

navim88…really….? step 1. bodies don’t apperceive the acknowledgment to a problem step 2. ill name the botheration “nullity” step 3. the acknowledgment to the botheration is “nullity” wow I’m smart.

Martin SpamerI’m a Computer Scientist not a Mathematician and a accustomed sceptic. About this is absorbing because of the agreement with how absent IS handled in Software Enginnering. Absent != 0 and is captivated alfresco the calibration of complete numbers. Absent is usually represented as which adeptness present a bigger accession than a new sym.

WillAll he’s done is achieve a name for a botheration to affectation the problem… I don’t ahead it absolutely solves anything.

Kirill A. WoroshilovAnd what does that guy ahead about L’Hospital’s Rule?

Emmanuel D.I am complete sceptical about such “theory”. First, it is absolutely confusing, and I don’t see how it can admonition to acquire some problem. if 1*nullity = 2*nullity, afresh nullity/nullity = 1/2 AND nullity/nullity = 2/1. But alike worse, 1 = 2*nullity/nullity. So you acquire to say that nullity/nullity is amorphous to explain this answer. Your transreal accession fails to do this, as far as I accustomed it. Second, aback it’s still confusing, Iit would acquire been bigger to delay for for algebraic affirmation afore teaching this aberrant things to pupils. This is about criminal. Aing year some added abecedary will arise with a access that says that 2 2 can be according to 5 for complete ample ethics of 2 and babyish ethics of 5. Will he be adapted to advise this to pupils afore achievement confronted to his collegues? I ahead no. Animate in this way is aloof aboveboard dangerous. Science and algebraic needs to be authentic afore they are able – that’s a basal fact. You additionally bootless to do this, and this is angled imho. Finally, abyss doesn’t absolutely admonition aback it comes to computers. How will you represent it (and both aloft and abrogating infinity) appliance a 32 $.25 integer? Or a 64 bit accumulation for that matter? Bethink you still acquire to chase the rules of 2-complement arithmetic… That’s activity to be absolutely hard. I accepting the band-aid is to accord them some adapted values, and to hardwire the calculus in the ALU – this is not complete able imo. I don’t appetite to say that the access is some accidental babble (I’m absorbed to ahead that a representation of these numbers is absolutely important), but I’d delay for bigger proofs – ie not proofs that are backed up with the IEEE FP standard.

SkuffIm no mathmatician (infact i attack to spell it). So im not absolutely abiding about all this 0 stuff. But i ahead the acumen algebraic exists is to assignment things out, allegedly starting at some bounded boutique and abacus chaplet or commodity etc…il barter one loaf for two fo these or what ever. So in my benightedness I attending at it simply, such as: Say we acquire One cake. We acquire 5 people. The block weight 500g. So anniversary achievement (if disconnected equally) gets 100g of block each. So, if theres 1 person, they get the able cake, 500g. So, if there arent any bodies to bisect the block between, doesn’t that beggarly that 500g is still left? Crude, Im sure. But, absolutely thats right? 500/0 = 500? I accepting this adeptness be allotment of the problem, in maths this aloof deceit work. I do acquisition that there seems to be a few holes in the aperture algebraic adjustment and we acquire hell angled on aggravating to accumulate it as the RIGHT way to do things. Its takes accession to try and prove added systems, it seems in todays angel we arise adored to use old(ish, perhaps, although bigger over time) methods that yes, acquire been approved and tested, but may be not absolutely correct. If a timberline avalanche in a copse and no ones heres it, does it achieve a sound. Yes, of beforehand it does, dont ask such cool questions ๐

YabaTheWhatThere is absolutely no charge for this abstruse value. Aboriginal off, any cardinal to the adeptness of aught is one. Why? Let’s say N is a number, and R is some accidental number. RxN^0 is interpreted as, “Multiply R by N aught times,” or added generally, “Multiply R by… wait, no, nevermind, aloof leave R alone.” Next, let’s abode the absorption of 0/0, or aught disconnected by itself. The simplest acknowledgment is that any cardinal disconnected by itself is one. Acutely computers acquire a botheration with this concept, so let’s access it from a added able standpoint. Computers acquire adversity abacus by zero, because 1/0 is infinite, and computers abandoned accord with apprenticed numbers. That’s the botheration designers would charge to fix. Instead of alleviative numbers as apprenticed values, tack on an aloft tracker. Let’s use oo to represent infinity, aback I’m autograph in a altercation box. The basal botheration is that 1/0 = oo. In apprenticed mathematics, that causes an error. However, 1 in a apprenticed adjustment is absolutely 1 not altered by any infinites (or not disconnected by zero). We could say that apprenticed 1 is 1 altered by no infinites, or “one with aught infinites” as a autograph version. Now bisect it by zero. The aftereffect is one with one infinite. Now bisect 1 by this result, and you get 1 (from 1/1=1) with -1 infinites (1/oo). Bisect this cardinal by zero, or accumulate it by oo, and you’re aback to 1 with 0 infinites, or apprenticed 1. To bisect by aught at any time implies that aught is, in fact, not an complete value, but artlessly an atomic value; it is so babyish that it is admired as nothing. This, from the bend above, would be called, “one with abrogating one infinites.” We could, of course, accumulate it by itself to get the value, “one with abrogating two infinites.” Accumulate this by oo, or one with one infinite, and you’re aback to one with abrogating one infinites. Accumulate by oo again, and you’re at one with no infinites, or apprenticed 1. Taking the absorption a footfall further, accede the simple blueprint (x^2)-(2x) 1=(y^2). In apprenticed math, that’s a simple botheration to resolve. What about if x = oo? The acknowledgment is that it’s still the exact aloft problem. The answer, y=x-1, still applies. Autograph out the equations, we’d acquire one with two infinites bare two with one complete additional one with aught infinites equals the aboveboard of “y”, absolute to “y” equals 1 with one complete bare 1 with no infinites. So what’s oo^oo? Accepting you’d charge to tack on a additional aloft adverse to the cardinal at that point. While I wouldn’t apprehend a simple duke calculator to handle this problem, any authentic calculator advised to handle the aboveboard abject of abrogating one should be able to handle infinites in this manner. Getting aback to the able affair of “nullity”, it’s basically useless. Abyss basically means, “One altered by some apprenticed numbers I was too absent to track.” If accustomed by the algebraic community, it could calmly be acclimated to prove that 1=2, or a array of added . [Gyeh. There are too abounding replies to this altercation already. Forgive me if accession has already said what I aloof said. It consistently seemed to me like a adequately attainable solution.]

AnonI’m belief in the Annual University Mathematics department. I would like to point out that this guy is not a mathematician and works in the computer science department. Appropriately any theories that he proposes are annihilation to do with the mathematics department.

David MellorWhy such skepticism? I’ll bet bodies would acquire said the aloft about the aboveboard abject of bare one, and attending how advantageous that is now (really!).

BlackTiger… Absolutely strange. If you are abacus commodity by 4 it agency “divide in 4 pieces”, isn’t it? Ok. What is aftereffect of “dividing in 0 pieces”? Aloof nothing. What’s amiss with it?

DecipherInventing a new appellation to accord with it, is not absolutely ytic it, is it?

AimeeTry a altered sym, sir! That one your appliance equals 1.618 and it’s one of my favourite numbers!

MaryMy compassionate of the complete numbers is that they don’t absolutely end. So how can aloft acquire a value? That would beggarly the end of the complete numbers, which is not possible.

NullityI acquire annihilation to say.

Albert EinsteinWhat is abyss disconnected by nullity? Abrogating infinullity?

ConfusedIf this botheration hasn’t been aboveboard for 1200 years, who aboveboard it 1200 years ago?

PythagorasIf the ogue of aloft (positive) is 1/0 afresh is 2/0 not two times infinity? This would be a aloft aloft by the algebraic rules that I know. This absorption can be extracted an infinitum. As a result, 1/0(1/0) is an complete infinity, additionally apperceive as an absurdity. Does this achieve any sense? Aloft is complete by ogue and accordingly annihilation is larger. Maybe, aloof maybe Mr. Anderson is 1/0 nuts. That’s it, the man is off his blinking rocker. Now for there complete issues of activity – aloof how abounding angels can fit on the arch of a pin?

D.V.1. if you apprehend his axioms you will realise that “nullity” is what bodies acquire been calling “undefined” for 1200 years. The axioms are identical. He aloof renamed the word. 2. if your affection pacemaker divides by aught you are NOT dead. there are things declared babysitter timers that displace microcontrollers aback things like that happen. 3. creating an commodity out of “undefined”, declared “nullity”, that behaves ogously to what we acquire consistently accustomed as “undefined”, does not admonition computers or mathematics any.

KhojiDr James Anderson wrote: “It is aloof an arithmetical achievement that 1/0 is the bigger cardinal there is. ” Rubbish. That’s about as allusive as adage that an orange disconnected by an angel is a pear. 1 is a quantity. 0 is the abridgement of a quantity. Appliance syms from the aloft afterwards adjustment for both of them creates the bookish apparition that they are both numbers, but they are not. Thus, the complete abyss building collapses aloft itself.

Beender DundatMy theorem: any cardinal (includig zero) devided by itself is 1, ex. 1/1=1, 123/123=1 and 0/0 = 1 and infinity/infinity = 1. Also, any cardinal (including zero) to the adeptness of 0 is 1. Annihilation devided by aught is aloft (positive or negative, depending on its sign). Clean and simple.

UnnessecaryStudentEhhmm… Thats aberrant – To acknowledge a new “number”/”letter”. I’m not adored about this solution. I’m sorry.

JaapHi, If this botheration is 1200 year old, afresh what does Pythagoras acquire to do with it?? And as physicist I did not see any new algebraic here.

AnonymousAny Java programmer will be able to see the affinity to Double.NaN (Not a Number) constant. This was conflicting by Sun atleast in 1996, could acquire been beforehand if done in added programming languages too. The abandoned addendum achievement seems to be that its achievement brought into the non-programmer world.

Brian MatthewsHere’s why ‘nullity’ doesn’t work: WHat is abyss disconnected by nullity? Well, it’s 1, isn’t it? On the added hand, this is additionally according to (0/0)/(0/0), which by simple maipulation of fractions is according to 0/0, which is nullity. So abyss according 1. Nonsense. QED.

SekkyGuys, this adventure is in no way affiliated to circuitous numbers. Circuitous numbers are no added or beneath artifical than the abrogating integers or rational numbers, they’re all aloof extensions to accommodate a superset. They are in no way like what is achievement adapted here, which by the way, is an embaressing abhorrence of absolutely nothing. Abstain all assay affidavit from the University of Reading.

Navid ZamaniI KNEW it! I KNEW it the WHOLE TIME! Never aback i aboriginal heard that there is an “exception” to all math, aback appliance zero, i acquainted complete able that this is wrong. Like a annihilate in the cast or 2 2=5… You apperceive it. I searched for solutions to it. But they mostly went with “something / aught = infinity_n” breadth n captivated the admonition about “something”, so by muliplicating “infinity_n * zero” you would get “something” back. Worked absolutely well, but there were problems with it…. (that i can’t bethink for now) I’m REALLY adored this happened! So i assuredly can acquaint my ex-teachers that *I* were adapted all the time! THANK YOU MR…. Anderson…? Oh… my…. GOD… I’s you Neo! You aboveboard the glitches! ๐

MikaelSo, how does this chronicle to the access of algebraic wheels; which as I bethink it additionally accord with 0/0 by extending the continued reals to accommodate this as a new bookish element?

Three Aerial Academy Algebraic Agents Mr. Gagliardo, Mr.This is not commodity new beneath the sun. 0/0 is undefined; but it can be additionally be advised indeterminant because it can be any value. 0/0 could, for example, be 7 because 7 x 0 = 0. It could additionally be -41, .2, etc. Calling it abyss is aloof a bit too cute. However it gave us commodity to ahead about.

Kyle BurtonI’m sorry, but there isn’t barring administration in accumulation assay

Funny ThatThis has to be a antic of some sort! Some abundant comments beneath though: Bob:”The diplomacy wont crash, but the alike abiding as hell will.” :0)

Dr Richard Daniel HillThis man is a charlatan and a crank

ライト0/0 = Nullity? Aing affair we know, he will acquaint us that .9~ =/= 1.

nullity.complex: defn: bodies with annihilation to do bIt does affect me that so abounding acute bodies feel the charge to shoot bottomward accession mans ideas….whether bad or good. Acutely little abroad to do with their absent lives. Its attainable to be a critic. And about every yst has arise up with the band-aid at some date in their adolescent lives. One things missing…why did these bodies do annihilation with their new ideas? Alike abundant minds had aboveboard problems in the past, but acquired no accepting for it because one has to see opportunity/value in such solutions. From my point of view: if i booty 10/5 = 2 and catechumen it to 5*2 = 10 afresh I would apprehend that 1/0 = ? could be rewritten as 0*? = 1 but accumulate by 0 gives you 0. This is what we’ve consistently been thought. We can additionally never acquaint if 1/0 is abrogating aloft or complete aloft yet both are possible. NULL is acclimated in computer programming to ascertain beggarly nothing/empty/undefined. Its allows blockage for the achievement of commodity of interest. Comes from the latin chat nullus acceptation “not any” Is it not attainable the assistant is aggravating to explain this access through algebra….. I cannot appearance the video so I do not know. And so what if its been discovered. I’m abiding its a attainable access to teaching this stuff.

JCAI admiration how Dr. Anderson handles (a complete number) (infinity) – (another number)-(infinity). Aback his infinity lies breadth it does, how does he handle it?

prober8if: 0/0 = ร so: 0/ร = 0 then: ร = 1 ??? nullity = accord ???

Adam BraunExpress it as binary.

AnonEvery acreage has a nullity. That’s basal abstruse algebra. One should be alert of bodies defining things calmly afterwards annual or affidavit – what you’ve got there is aloof afterwards masturbation. Abstain algebraic sensationalism at all costs!

MattI came up with the aloft band-aid years ago except I acclimated the attribute “Doh!”.

Thom HowesSimple question, if the numerator and the denominator both approached 0 at the aloft rate, wouldn’t the aftereffect consistently be 1?

SimonIt’s authentic that abacus by aught does annual an applesauce in programing, but any programer that has every accounting a diplomacy added circuitous than “Hello World” (Tradtionally the aboriginal diplomacy you anytime write), will apperceive to allurement the applesauce afore it occurs. So it can be dealt with gracfully (i.e. allotment a defaul bulk instead), rather than crashing. Any of the avant-garde or Commodity orientated programing accent will acquire expection administration congenital into the it for aloof this array of problem. As a computer scientist, I would acquire hoped Dr Anderson would apperceive better.

Mutant RobSo has he vetted this absorption in acclaimed maths journals amid added mathematicians, or is he appliance his adeptness as a academy abecedary to appoint dishonest annual on his students, abundant like “rational trigonometry”?

ChrisNewton? Fool. Pythagoras? Useless. Anderson? God. Eat your affection out, creators of mathematics as we apperceive it!

The MoleSo: Ships and planes unexplainedly abandon in the Atlantic. Let’s acquire there’s a breadth which lies alfresco the accustomed space/time band and accord it a name. Now the disappearances are all explained aloof by adage “Bermuda Triangle”.

LJLIt’s been a continued time aback my Avant-garde Access classes, but doesn’t a cardinal lying OFF the cardinal band breach the adage of Completeness? I acquisition it adamantine to acquire Dr Anderson would acquire artlessly disregarded the best basal adage in avant-garde mathematics, but that’s absolutely what he appears to be doing. Before contradicting the use of the appellation cardinal here, let’s face it, annihilation acclimated to represent a bulk is a number, alike if you anxiety it a non-number. I acquire a botheration wrapping my academician about a bulk disconnected by a bulk bearing a non-value. One adeptness as able-bodied say 6 10 = a dog. This is actionable – or afterlight if you adopt – a cardinal of concepts that the all-inclusive majority of mathematics, from simple ciphering to avant-garde access – relies on. I won’t go so far as to use the aspersing acceding presented by added commenters, but I absolutely ahead bottomward this from the animation lath to a schoolroom afterwards associate assay and accustomed accepting is capricious at the least. I do apprehend that the authentic botheration of assay by aught is a decidedly aberrant one, so I can acquire the beatnik approach, but there are times aback either infinity, abrogating infinity, zero, or 1 tend to “fit” animal intuition – which we all apperceive is not consistently alike close, but for real! I do ahead there’s a way to handle this, but I ahead it’s maybe aloof a little added circuitous than “Hey! Let’s achieve up a new (non)number!”

GooseAnyone apperceive of a acclaim agenda with this affectionate of absorption rate??

No bodyTake the pairs (a,b) of complete numbers. Two pairs (a,b) and (c,d) are “equivalent” if there exists a non-zero complete cardinal x such that c=a*x and d=b*x. This is an adequation relation. Let “a/b” denote the chic of (a,b). Let the “product” of “a/b” and “c/d” be authentic as the chic of (a*c, b*d). Let “nullity” be the chic of (0,0). Is there commodity added in the abyss theory?

Mark JohnsonCan we ad-lib some new belletrist to the alphabet as well. Apologetic but “making up” a new cardinal does not breach bisect by 0. The acknowledgment should arise out as an applesauce and thats the way it should stay.

its meI too acquire aboveboard an old age problem. The acceptation of activity which I anxiety Liath. It is absolutely simple now that we acquire that Liath happens amid Activity and Death ๐

Nathan GerberSo ok if this is solved, aloof how do I booty this new bulk and abide ytic a problem? Basically all this is accomplishing is demography abroad a “divide by zero” applesauce and replacing it with a “nullity” or “negative aloft to complete infinity” error.

QrizWow…some loooooong explanations there. 0 is commodity we fabricated up. abacus by 0 (for example, abacus 9 into groups of 0) would get you infinity. So you alpha ambidextrous with kinds of infinity, which is additionally a concept, not a apprenticed value. Aught and aloft are artificial, and they admonition us represent and assignment through problems. Like accession said bottomward there, algebraic is all definition. There isn’t a “right” acknowledgment unless it fits these definitions.

DaveHypere. I had to appearance added affidavit in cast 5 – but I doubtable this dishonest has no proof.

Stephen Leary0/0 is Not A Number. This is able-bodied authentic in accretion science/Maths etc. “Nullity” is aloof a redefinition of this and has been about for years.

CharlesNice joke. But you can’t put a abundance on Nothing, that should be aloof about Attainable to anybody about achievement

Carolus HolmanIf I booty an Orange, and bisect it by Noting or 0 or don’t cut it, I still acquire a able orange. So in my believer academician 1 orange disconnected by annihilation is still an orange. I am afraid that the British are so gullible, but afresh again, I am British.

JoeDr Anderson has done annihilation but add a new characters that was not needed. His ogue of 1/0 as Omega is flawed, as there are aloft complete numbers. Avant-garde computer programmers use barring administration to administer the “divide by zero” error, and this “new” absorption adds annihilation to that science.

Cracked out winoDude, Nullity [email protected]#$ Professor acute guy for preZ!

Stuart Adamantine ManThis guy needs to amalgamate up. Seriously Plus Lee and Bag do some work!

Adventure ProblemThere are twenty apples in a bag. Neither Rick, Jane, Sam or Betty appetite any of the apples. How abounding apples does anniversary achievement get? 20/0 = nullity Each achievement gets abyss apples.

Apathetic of EducationSorry, this guy is a fool. Abyss is not a complete number, and you cannot adeptness it from abacus by aught BECAUSE YOU CANNOT EVER DIVIDE BY ZERO TO BEGIN WITH!!!

ummmummm complete player? are you serious?

MikeThis is aloof stupid, annihilation has changed, we aloof now acquire a name for the no non-value that results. You may as able-bodied anxiety it applesauce so that at atomic the calculators are still adapted

C R HulcherZero is a abode holder, never was a “number”!!!!!

JoeThis is not clashing astrophysicists who, aback their numbers don’t work, aloof theorized commodity they anxiety “dark matter” which does annihilation but ample in the gaps in their equations.

ChocoSo abounding comments achievement from the computer programmers’ affected – how abounding of you can candidly say the computer languages from which you draw your examples are mathematically rigorous? When was the aftermost time a mathematics assistant wrote “Type mismatch” on the blackboard? A bit of annual up on e.g. Peano accession is bare afore arduous Dr Anderson’s working.

de GraafSo… does this crop an acknowledgment for the Le=orentz-Fitzgerald blueprint (that yields a assay by aught aback the acceleration of an commodity matches that of light)?

TofuHmmm…. I acquire an insolvable problem. I KNOW! I’ll aloof achieve up a cast new aberrant announcement and affirmation that that is the answer! His step-by-step “detailed” archetype doesn’t breach 0/0. He aloof gives a able placeholder instead of an applesauce message. Also how can he anxiety “nullity” a cardinal if it doesn’t abatement on the cardinal line? Heck I could say an angel is a cardinal now and use his aloft argumentation to validate my theorem.

Gunnar GregerDivide aloft by infinity: Infinity/infinity=0, or is it? Ahead about it. 0/0=Infinity or is it 1? The solutiuon is hidden in infinity?

Peter Tettweiler, Hamburg, Germanyto be honest: no!

Shady TarekIs there any activated problems aboveboard with this ? I beggarly ok there’s a new cardinal now what does it do !

Matt FletcherExtending the acreage of cardinal by abacus adapted elements (e.g. infinity) is a basal and atomic operation in alegbra. There is absolutely annihilation new achievement at all. The BBC should abandoned abode authentic advances arise in peer-reviewed journals. Anderson’s assignment seems abandoned to be arise via his claimed webpage breadth his cardboard allegedly demonstrates “the achievability of assay by aught and challenges the clairvoyant to acquire it”. Not the accustomed diction for a abstruse cardboard with commodity 18-carat to say. Please stop giving this nut chargeless publicity.

DavidJust do what I do – aback in agnosticism what do you get if you altered 6 by 9? 42. (And for those who don’t see the affiliation – 6*9(base 13) does absolutely according 42 :) Thank you to the astern abundant Douglas Admas for that Gem. 1/0 or 0/0 will abide NaN for a continued time yet. Until C supports abyss – no computer will angle a adventitious of compassionate the absorption at the basal operating adjustment level.

Alexander RozmanHow does authoritative up a new attribute breach the botheration of computers diving by zero? Aloof how does this access beforehand encoding abyss in bifold or d accession operation on it?

TRexThis is great, but I don’t get it, can you abode a job aid for it?

Morten V ChristiansenI am not abiding what Dr. Anderson has done, but in accepting the absorption is not problematical. Several non-standard interpretations of cardinal access exist, some with complete sets of “alternate zeroes” or infinitissimals. They are provably as connected as accustomed cardinal theory. This is no altered from non-standard set access or non-euclidian geometry. If Dr. Anderson has created an accustomed the bendability of such a system, which is attainable abundant to be accustomed by academy children, I ahead that is a complete nice accomplishment. It does not accommodate mathematics, but it is complete nice work.

AlphaAXPThis access looks itself a lot like the own aftereffect it referes to: a nulity. ”A” quantity, alike if abstract, can be defined, not “Any” quantity. activity but not original. algebraic already owns a attribute for “Any value”: it’s a basal “A”O upside down.

Dr. OH RLY ObviousTo: Dr. Obvious, If you times a aberrant cardinal a rational, you get a irrational.

RouDyThe 2nd footfall afore the latest is apocryphal (1/0 is impossible). And 0/0 is air-conditioned too. (sorry for my bad english, i’m french)

Tim PozzaWill the new cardinal acquiesce us to annual aback aloft touches itself in amplitude and in time?

ZipNot a Cardinal is basically like a workaround to accumulate an appliance from aition a basal software engine. That’s about it. It’s not a algebraic affidavit of anything. Basically, all he did is to adduce a adjustment that can be acclimated in bisect by aught situations, that’s it. There’s no acumen for about all of these assault replies. It is true, though, that this allegedly isn’t activity to magically fix software glitches of any affectionate in avant-garde managed code. Maybe it would acquiesce lower affiliated cipher (assembler, c, etc.) to not acquire to t bisect by aught errors on systems with adapted firmware that handles the absorption of “nullity”. That’s about it though. The botheration afresh becomes astern compatibility. ๐

Michael ClaytonQuoting the Dr. Anderson “It is aloof an arithmetical achievement that 1/0 is the bigger cardinal there is.”. That is aboveboard RUBBISH. Patently FALSE. Here’s the proof: 2/0 > 1/0

SebHaving 0/0 as amorphous is advantageous as you can’t use it. If you ascertain it as a attribute bodies use it in algebra and you end up in all kinds of 1=2 kinds of problems, throwing out an applesauce from your calculator is a able assurance you fabricated a aberration and should go aback and fix it.

JMSI’m able to see that his PhD wasn’t in mathematics. That said, the annual that the appellation “Doctor” brings should be acclimated wisely, and absolutely not in misinforming the accustomed public, let abandoned accessible children. This fabricated me complete affronted indeed, to say the least. Angrier still, aback I apprehend his affidavit on “transreal ysis”. Again, I’m animated that these won’t be arise in any admirable algebraic journals. What he has done is not mathematics; it is added anxiously accompanying to the acreage of linguistics: don’t acquire a chat for something? Let’s achieve one up and afresh use it to explain the aloft word. He has absitively that the botheration of abacus by aught can be aboveboard by adage that if it could be solved, its acknowledgment would be “nullity”. Blank the achievement that abyss afresh breach best capricious laws, he has not acclimated abyss as a adjustment for ytic any complete problems. Some acquire said that his “work” is affiliated to the assay of the abstruse cardinal i (the aboveboard abject of -1). However, i is advantageous in ytic abounding algebraic and real-world problems; abyss absolutely is not. His affidavit affirmation to ad-lib a new anatomy of accession that allows the use of his new number, but in absoluteness they artlessly add axioms to the complete set so that he gets about the problems befuddled up by nullity. Furthermore, he envisages the computers of the aing appliance his new anatomy of accession so that the “NaN” applesauce is replaced by “nullity”. How does that breach the problem? Alike if the computer afresh knows how to use it in equations, it won’t accord any reasonable answers since, by his own calculations, any blueprint involving abyss has an complete cardinal of solutions. How cartel he masquerade as a mathematician? How cartel he decay admired assay grants on a commodity so useless: commodity that, clashing authentic mathematics, has no scientific, abstruse or activated value? I am adored to see that there are an cutting cardinal of comments on this folio abusive his assignment – best of these bodies allegedly acquire beneath apprenticeship than he but they can calmly atom the fallacies in his absolutely ludicrous, beatnik theory.

cies breijs”-Inf” and “Inf” are no numbers, so “Nullity” is not a cardinal (“NaN”) aswell. We could achieve a aberration amid altered “NaN”‘s and anxiety them “-Inf”, “Inf” and “Nullity”, but will this achieve sense? We we be able to do somehtings that was avant-garde undoable (like circuitous numbers accredit us to do)? I don’t ahead so: NaN 1 = NaN NaN * 2 = NaN this authority authentic for any NaN, so this renders them useless.

WalemfrickGreat work! If abyss extends from abrogating aloft through aught to complete aloft afresh it is a authentic acknowledgment for any botheration not aloof this one! 1 4 = NULLITY!, the abject of 123786476362783456734 = NULLITY! If this gets accustomed cipher has an alibi for scoring beneath than 100% in Mathematics anytime again, apologetic NULLITY%.

All this is complete usefullPerspex machine: VII. The accustomed perspex machine James A. D. W. Anderson The Univ. of Annual (United Kingdom) (published online Jan. 15, 2006) The perspex apparatus arose from the affinity of projective geometry with the Turing machine. It uses a complete arithmetic, declared transreal arithmetic, that contains complete accession and allows assay by zero. Transreal accession is redefined here. The new accession has both a complete and a abrogating aloft which lie at the extremes of the cardinal line, and a cardinal abyss that lies off the cardinal line. We prove that nullity, 0/0, is a number. Appropriately a cardinal may acquire one of four signs: negative, zero, positive, or nullity. It is, therefore, air-conditioned to encode the assurance of a cardinal in one bit, as floating-point accession attempts to do, connected in the adversity of accepting both complete and abrogating zeros and NaNs. Transrational accession is connected with Cantor arithmetic. In an addendum to complete arithmetic, the achievement of zero, an infinity, or abyss with its alternate is nullity, not unity. This avoids the accustomed contradictions that chase from accepting assay by zero. Transreal accession has a anchored algebraic anatomy and does not acquire options as IEEE, floating-point accession does. Best significantly, abyss has a simple semantics that is accompanying to zero. Aught agency “no value” and abyss agency “no information.” We altercate that abyss is as advantageous to a artificial computer as aught is to a animal computer. The perspex apparatus is advised to activity one band-aid to the mind-body botheration by d how the accountable aspects of apperception and, perhaps, the able of apperception relates to the geometrical aspects of anatomy and, perhaps, the able of body. We assay some of Turing’s writings and appearance that he captivated the appearance that his apparatus has spatial properties. In particular, that it has the acreage of achievement a 7D filigree of bunched spaces. Thus, we apprehend Turing as assertive that his apparatus relates ciphering to geometrical bodies. We abridge the perspex apparatus by substituting an aggrandized Euclidean geometry for projective geometry. This leads to a general-linear perspex-machine which is complete abundant easier to diplomacy than the aboriginal perspex-machine. We afresh appearance how to map the able of perspex amplitude into a assemblage cube. This allows us to assemble a fractal of perspex machines with the cardinality of a real-numbered band or space. This fractal is the accustomed perspex machine. It can solve, in assemblage time, the awkward botheration for itself and for all perspex machines instantiated in real-numbered space, including all Turing machines. We adduce an acceding that has been proposed to assay the authentic absoluteness of the perspex machine’s archetypal of time, but we achieve no affirmation that the authentic cosmos works this way or that it has the cardinality of the perspex machine. We leave it that the perspex apparatus provides an aerial apprenticed on the computational backdrop of authentic things, including artificial computers and biological organisms, that acquire a cardinality no greater than the real-number line. ยฉ2006 COPYRIGHT SPIE–The All-embracing Society for Optical Engineering. Downloading of the abstruse is adequate for claimed use only.

MattTo me, it looks like the acknowledgment is still the aloft as it has been for the able 1200 years, he’s aloof absitively to draw a doodle at the end claiming its the attribute for ‘nullity’

Gunnar GregerDivide aloft with infinity:infinity/infinity=0 or is it zero?Think about it.

Richard Bremner, Aberdeen*Announcement* I acquire aboveboard the botheration of what is North of the North Pole, it’s declared Northity. Anybody rejoince.

mikeWasn’t this commodity able for 04.01.2007 ?

Michael McGuireThe man is a crank on the affiliated of the “squaring the circle” crowd. The accustomed bulk of 0/0 is amorphous for several able affidavit that anyone with an compassionate of cartography or alike basal calculus should understand. Replacing 0/0 with a adapted attribute would absolutely actualize added problems than it would fix. I acclaim a quick attending into the works of Cantor and/or Komologorov for anyone who is absorbed into avant-garde theories of aught and infinity.

Wayne SmallmanAm I the abandoned one to absolutely underwealmed by this new access of nothingness? If all he’s accomplishing is authoritative up a new non-number, I’m hardly afraid by him ytic this problem. Almost any botheration can be aboveboard by aloof authoritative achievement up to fit the problem. Some associate assay adeptness be added telling…

HONKHURFEY DURFEY baby, congrats on advancing up with a admirable new name for an already authentic concept. There isn’t annihilation new achievement except a asinine name and a done up professor.

Dr James AndersonLet me try to acknowledgment the comments acquaint above. I acquire authentic a new number, abyss = 0/0. I acclimated a sym, basal phi, to denote that number. The attribute I use is irrelevant, what affairs is the ogue of the number. Iโll say a bit added about this cardinal in a moment, but aboriginal letโs get ablaze what we are talking about. I additionally authentic aloft as 1/0 and bare aloft as -1/0. This is connected with abacus a non-zero cardinal by anytime abate numbers aing zero. The geometry of this adjustment is apparent in the video. The cardinal band stretches from bare aloft to additional infinity. It does not blanket about into a loop, it does not yze complete and abrogating infinities as adverse poles in a projective geometry (though it is attainable to do that if you appetite to). The geometry is absolutely as apparent in the video. The cardinal band stretches all the way from bare aloft to additional aloft in a beeline line. The new number, nullity, lies off the cardinal line. I drew it aloft zero, but it can be fatigued anywhere that is not on the line. Its geometry can be accustomed in the aloft way that the cardinal i, the aboveboard abject of bare one, can be understood. All of its algebraic backdrop can be fatigued as pictures in according geometry. Some bodies use j to announce the aboveboard abject of bare one. The attribute does not matter, what affairs is the ogue of the number. Once I accustomed the geometrical annual of the new numbers and accustomed how to accomplish on them as fractions, appliance pencil and cardboard methods, I wrote the able lot bottomward as ytic rules or axioms. Dr. Andrew Adams from Annual University and Dr Norbert Voelker from Essex University helped me beforehand the axioms. Norbert translated the axioms into academy adjustment argumentation and acclimated a computer to prove that they are consistent. The axioms accommodate the able of accustomed arithmetic. This is complete important, it agency that annihilation that can be affected appliance accustomed mathematics can still be calculated, but now it is attainable to annual added things as well. Iโll say a bit added about this later, but adapted now letโs see why abyss is a number. There are abounding agency to ahead about numbers (and I use whichever way is able at the time), but one of the simplest is to say that a cardinal is annihilation that obeys all of the axioms of arithmetic. Therefore, abyss = 0/0, aloft = 1/0, and bare aloft = -1/0 are all numbers because they obey all of the axioms of my new arithmetic. I ahead the angel has acclimatized on oo as a attribute for infinity, admitting aleph and omega are additionally acclimated for altered kinds of infinity. If you appetite to run a antagonism to acquisition a bigger attribute than basal phi for abyss afresh go ahead. If itโs a nice attribute I will use it in my authentic papers. In my axiomatisation it is authentic that aloft is greater than zero. From this it follows that aloft is greater than all numbers. Iโll put a affidavit at the end of this message, but letโs be ablaze on what this means. The acreage of achievement consistently big follows from the achievement that a complete cardinal is disconnected by zero. It is not all-important to ascertain consistently big by any added means. It is not all-important to use calculus or set access to ascertain consistently big. It is not all-important to use any abstruse absorption of bigness. It is aloof an arithmetical achievement that 1/0 is the bigger cardinal there is. As I said, there are altered kinds of infinity. It is attainable to add these to the cardinal line. They are all abate than 1/0. In some areas of mathematics a bigger aloft is authentic according to the axioms of that area. Several areas of mathematics use the attribute basal omega to denote the bigger infinity. Its backdrop depend on the axioms in use so they can adapt from breadth to breadth of mathematics. My aloft shares the acreage of achievement the bigger infinity, so you can use basal omega as a attribute for it if you appetite to, but the backdrop of my bigger aloft chase from the backdrop of my accession and not from annihilation else. Some areas of mathematics ascertain consistently babyish num

Tormod HMath is all about definition, and authoritative connected roules to chase in every situation. to affirmation that a codicillary annual in computer cipher is acclimation it; is aloof ignorance. with a algebraic accepting defining how to handle this situations can beforehand a lot. it is important to acquire that algebraic is absolutely altered than computer calculations; like with diffenecials, it is attainable to do “calculations”, but with constraints. if you breach the constraints you alfresco accustomed algebraic and you are responible for you results. With a abounding authentic accepting about x/0 we can change computer science too. we aloof charge CPU-core suport, and/or ascertain som agent rooms. Major leaps in science history is done by alteration the perseption, not claiming that we can cope with it as it is. like the theroy of relativity. ( apologetic for the spelling errors. Dyslectic, but not addled ๐

MIchael ChizmarI could not attainable the video so I do not apperceive if this is relevant, but is there there a affidavit aloft the ogue of nullity? Or, is this aloof a digest of what is already known, like (a antecedent affiche stated) NaN?

RenAwww I aboveboard it years ago but didn’t ahead to advertisement it.. 1/0 = WTF? As you can see, my While Authentic Float is accession chat undefined, and the Float lets us apperceive it’s a apportioned number.

Toshke from SerbiaThis is absolutely addled like all agnate proofs. Of beforehand it didn’t prove anything, he aloof created a new number, and aloft that cardinal can be anything, from -inf to inf. It is not activity to admonition any calculations. Poor children, at age of ten, they are achievement able of infinity, they should do it in aerial school. And this ‘nullity’ ๐ Balloon it!

@ FredI accede how do you repersent Abyss in bifold or alike hex. The added botheration is he didnt alike breach the blueprint he aloof fabricated up a new commodity to accommodate a solution.. and abyss has consistently existed its declared NULL so in aspect he has aloof renamed the solution.

Dave GowerThis is, indeed, rather sad. 0/0 can be authentic if a activity that banned to it (such as sin(x)/x) is able-bodied authentic and continuous. annihilation else, as mentioned aloft is artlessly NaN. They’re not authentic and allegedly never will be. The affidavit is diaical. 0/0 = -0- accordingly 0/0 = -0-. Yikes.

ytillunIf the aeroplane divides by zero, my pacemaker crashes ๐ or, the pilot has to accord with “we are abyss meters from the ground. Columnist any key to blast now, or delay for abyss annual for an auto-crash” How I ambition my coffer disconnected my $1 antithesis by aught and told me that I acquire complete money ๐

ComputingProfessorUm, this is annihilation new. We acquire the absorption of nan (not a number) and alike do accession with it – any time one of the operands is nan, the aftereffect is nan. Fits nicely. So this is aloof a new name for commodity that has been about for a while.

van de WeertIn my canicule as a apprentice we talked about this aloft botheration and authentic a band-aid to it. We declared that cardinal “van de Weert”, in advertence to a abundant awful teacher, we had endless of fun with it. And now this …. abecedary tells his accepting this bashed ass allocution of us is authentic abandoned appliance a altered name? I anxiety it cool, but I agnosticism any austere mathematician is activity to booty it seriously.

RobThe band-aid contains 0/1 x 1/0. But his ogue states that 1/0 is complete infinity. So it’s 0/1 x infinity. But we all apperceive that 0/1 = 0 and 0 x ‘anything’ = 0. So the band-aid is 0. Is it absolutely all-important to ‘make up’ a new number? The accuracy is that he’s aggravating to change the rules. 1/0 is NOT complete infinity! It is able-bodied accustomed that 1/0 is ‘undefined’. I benevolence his students.

Brian K.Yes, at aboriginal i thought, “pretty cool”, but afterwards annual these comments, altho abounding are a lot meaner than they charge to be, i do see now that no botheration was absolutely aboveboard here. I mean, if you’re depending on flight systems software, you’re activity to acquire to t a “nullity error” aloof as abundant as you would a “divide by zero” error. How would abyss bear thru the draft of your algorithm??? Explain that and maybe i’ll adapt my opinion.

Tasty WheatIf any cardinal disconnected by aught equals nullity, afresh what does any cardinal disconnected by abyss equals to? Bisect by abyss error? ๐

Blast RadiusThe IEEE accustomed already defines 0/0 as NaN, which seems able enough. Abyss solves annihilation and is artlessly an about designator that this assistant invented. Unless “nullity” can be acclimated in complete algebraic equations usefully, it is absolutely useless. Bob has it complete aback advertence the uselessness of this non-number.

JohnComputers CAN bisect by zero, if they use IEE754 bifold floating-point accession (which about every computer does). x/0 is complete aloft for complete x, abrogating aloft for abrogating x, and NaN (not a number) for 0/0.

Lumocolour O’ShaugnessyWill this new fangled accoutrement admonition me get a bigger allotment of a aggregate pizza?

MikeI already aboveboard this botheration a continued time ago. The acknowledgment is 0 AND whatever the numerator is. Where’s my Nobel Prize?

CCMathematicians anxiety that compactification of the complete line, annihilation new!

Ibzno admiration i consistently flunked in maths!

a hardly beneath abecedarian mathematicianTake a chic on complete assay or admeasurement theory. We assemble algebras that can handle assay by aught all the time. Dr Anderson? This “new theory” is decades old. I abstruse it as an undergrad, from advisers who abstruse it as undergrads. And it absolutely isn’t yours.

Dr DubeyActually, some authentic mathematicians had anticipation of affair absolutely some time ago (Sometime geometricts in the 19th aeon I believe).

aberration guythis is crazy..if this is anesthetized by the all-embracing association afresh let me adduce a access defining aloft aloft aloft as “ellipsis”..

JDHe may be in the computer science administration but he appears to be absolutely apprenticed of avant-garde assurance ytic software techniques. An auto pilot will not “stop working” if it tries to bisect by zero, the software will t the activity and try to do commodity sensible.

olLol! Thats aloof a nice joke! ๐ Of course, the “nullity” cardinal is accustomed for a continued time (it is usually declared “undef”) in best programming languages. The funny affair is to ahead that bodies at the BBC buy this!!! :-)))

XpucmoWhat I acquisition advantageous in his absorption is that the new cardinal could achieve it easier and added accustomed in programming languages to activity results/events which are currently handled by exceptions. Additional it is consistently easier to use a appellation “XYZ” than “the accident which occurs aback you do this and this with that and that” – I ahead this is declared absorption ;) Also, the complete achievement that this access provokes such a bent acknowledgment and polarized opinions agency that it IS a new idea.

Ngrh8rWe acquire a name for this “nullity” and acquire had such a name for years. That name is NaN. Apprentice it well, Anderson. You are no inventor, you are not heralding a ablaze and new algebraic theorem. You are artlessly giving a new name to commodity association from the computer affected acquire accustomed for years.

noragree with u Caska adeptness admonition the computer programing and could be absorbing there.but for mathamatics not abundant admonition lol

a uk academy studentWhats this guy thinking? Aboriginal of all he thinks hes aboveboard one of the best difficult problems ever, doesn’t he ahead that any mathmatician over the able about abounding years has anticipation ‘hmmm lets aloof achieve up a chat for this and it’ll all go away’ Candidly like accession bottomward the comments annual has declared how is this to be represented in binary? I feel clumsily apologetic for the kids achievement able this, abounding bodies in my antecedent algebraic classes and I acquire said why not aloof achieve up a chat for it; it doesn’t work!

Tomek PerlakWell, the absorption itself seems ambrosial – it’s aloof a new sym. Just like there isn’t “really” an ‘infinity’ – there isn’t “really” a ‘nullity’ – but it helps to explain something. (Does it?) I would attentive disagree with Hubert J. – IMHO, there is not absolutely a aberration in this alternation of anticipation – please, apprehension that this new attribute is acclimated to “simplify” the zero-to-the-power-of-zero expression. Abandoned that. Anyways – I’m affectionate of a ytic about some added expressions – can the ‘nullity’ be acclimated in, say: -0- 12 = … ? -0- * 3 = … ? Or are we talking achievement about a absolutely new set of numbers, about like with the circuitous numbers?

Johan Krรผger-HaglertThis isn’t news, and it acquire allegedly been aboveboard continued ago. Java for archetype sets a NaN-flag aback you bisect by zero, NaN continuing for Not a Number. Afterwards you can calmly assay for such cases and handled them in whatever way you ahead is appropriate, the important agency is that the diplomacy keeps on active instead of crashing.

!!!defining a new attribute doesnt achieve up a access

Prasob.kI don’t ahead this is possible.This absorption of continued complete band is already there in mathematics.ie “real band abrogating aloft complete infinity”…I don’t acquire what is atypical about it!!!

BobbinsGreat, yet accession headline-worthy accumulation of debris spouted by accession who acutely hasn’t “got it”. Aback will the columnist assuredly see through this debris and stop columnist such ?

BadbarI had that access for a continued time but my anwser is 1. Because if you bisect x with x you get 1 as awnser. If you bisect 0 with 0 you get 1. If you ahead like dr anderson with the adeptness adjustment were 0 adeptness to 0 is 1. That the anwser.

Jyri VedruWhat is achievement aberration from MATLAB language’s attribute NaN (not-a-number)? MATLAB has been acclimated it for a while.

Southampton ECS anonymousYou ‘could’ apparatus abyss appliance the “NaN” (not a number) affection of the IEEE amphibian point specification, accepting ve complete as 2^149 and โve complete as 2^-149. However, why not artlessly assay your denominator afore appliance it?

Ciaran Fowleythis deceit be declared a ‘solution’ as it aloof authentic 0/0 as nullity, you anxiety the achievement of abacus by aught abyss first, afresh acutely if you bisect aught by aught you will get abyss (which you aloof authentic in the aftermost sentance). you adeptness as able-bodied anxiety it peanuts, not nullity.

EnginerdLooks like someone’s aggravating to get some disproportionate fame. What a decay of my time watching that video and commenting on this so declared theory. Arise up with commodity that affairs in the complete world…not these abhorrent examples about affection pacemakers and alike crashes. OK I’m done.

CrapolaI ahead I’ll go bottomward Dr James Anderson’s avenue and anxiety the ytic aftereffect of the annual authentic or apocryphal ‘Crapola’ and appropriately acquire invented complete compression, accord me a doctorate, captain and a massive admission now!

Kim TherkildsenU charge be joking.

Dr S.I ahead its air-conditioned and ambagious to advise accouchement commodity like this. Stick to authentic maths please, not some gimmick. I ahead you’d charge to absorption algebraic assay (and apperceive added about cardinal systems) afore achievement able to adjudge whether his ‘proof’ is authentic anyhow. Maths is an amazing subject, I would not appetite my abecedary to achieve achievement up anniversary day…

Mr SpockThe appliance of Dr. Anderson’s assay is “nullity”.

retiariusWhen I was a boy (Here’s one from the ”young-whippershapper department”), we programmed aircraft simulation systems for NASA (in Fortran and accumulation language). These were ytic models angry to realistic cockpits that confused and shaked assay pilots — they about tried to divide-by-zero due to programming bugs, poorly-understood equations of motion, etc. So, in “real life”, aback threatened with div-by-zero infinities, the motion actor didn’t aloof accident the pilot into the berth coffer but rather gracefully smoothed the aboriginal acquired into relative calm by blank all agenda computer output, inn favor of an og “mechanical limiter” override.

David StevensI will not acquire any affidavit that has been arise on a proprietary (realplayer) codex, breadth is the proof! Real mathematicians do not advise kids until the algebraic association has complete there proof, alike if this is accustomed to be authentic i ahead he is achievement complete capricious teaching cryptic methods that are not in the “curriculum” its aloof aboveboard capricious he should be abeyant awaiting an investigation.

ArjunDr Anderson’s Axioms: 1/0 = Inf, -1/0 = -Inf and 0/O = Nullity Using these axioms.. 0 = 0 * 0

Gerard KrupaThis man is out of his algebraic league. He has acutely based this ‘proof’ not on algebraic rules but on the IEEE 754 accustomed acclimated in best microprocessors that defines 1/0=infinity and -1/0=-infinity. In authentic algebraic acceding aloft is non a cardinal and about advised to be unsigned. Incidentally, to deomnstrate how authentic IEEE 754 is, it additionally defines 0 and -0 as two altered numbers. As for accretion it does not bulk in the atomic whether you represent the aftereffect of a assay by aught as infinity, -infinity, NaN (Not a Number, a attribute already acclimated in computer science to represent an baffling result) or some new attribute fabricated up by an bookish attractive for his 15 annual of fame, you still acquire to handle it as an barring and not backpack on aggravating to assignment out calculations based on a non-number.

FIN AnonymousThis is acutely aloof a antic by Dr Anderson (I hope). Actually abounding bodies allegedly arise up with this absorption of ‘nullity’ at some point of their lives. I bethink cerebration about this botheration with my acquaintance aback we were 11. We came up with the aloft idea. Later, aback annual ‘real’ algebraic books at the age of 16 we abstruse about Riemann angel and were acutely adored with the achievement that we had arise up with agnate annual earlier. If accession takes this commodity seriously, I achievement he abandoned considers if it would be a usefull affair to advise to children. NOT that it would acquire ANY MATHEMATICAL significance. I abandoned ahead that this should not be tought. Instead accouchement should abandoned be encouraged to appraise the botheration of abacus by aught (and additionally added ‘problems’).

QuicoHey BBC, the Innocents Day is the 28th, not the 6th. You absent by 22 days. Does any of your computers already implent this access on its calendar’s algebraic engine? Keep in apperception this new is in the “People” section, not in “Science” section, so whats accordant achievement is the Dr accomplishing “something”, not the “something” he does. Adequate to the Yellow pages. Ok, no added joking. The Dr uses acceding ment to appearance the complete breadth some sequences beforehand as if they were accustomed numbers adequate to be acclimated in accustomed arithemtics, and this is a HUGE error. There should be some chargeless sits on any Berkshire’s 6th Anatomy Academy algebraic beforehand for the Dr and the journalists advertisement this to booty advantage of.

Somebody987This is stupid. Introducing a new cardinal that would represent commodity is not a solution. And on the added side: Computers CAN DIVIDE BY ZERO (IEEE accustomed for amphibian numbers) – the aftereffect is a adapted “number” declared NaN (not a number)! So this botheration with introducing a new bulk has already been “solved” continued afore this (but it’s not so practical) and accordingly don’t acquire to this hoax.

Ludovic ClaudeActually there is annihilation new here. In abounding computer languages, you acquire a attribute that’s declared NaN (Not a number) and this is the aftereffect of some air-conditioned algebraic operation such as 0/0. The diplomacy doesn’t blast aback you anxiety 0/0, it artlessly acknowledgment NaN (or let’s anxiety it -0- like this guy did), and afresh it can abode that there was an applesauce to the user. So this ‘number’ is abandoned commodity is abandoned that’s able to use with computers, but it’s absolutely not a authentic accepting and has no acceptation in cardinal access (the annex of maths that tries to explain and formalise numbers).

sulanJust accession atomic “discovery”. Anybody can ad-lib a attribute and anxiety it a band-aid of a problem….

joeFrom a computer science bend any programming accent acclimated to actualize software can ascertain and t ‘divide by zero’ errors. This new abyss attribute has no advantage to software. From my apprenticed compassionate of mathematics, I would ahead that abyss is agnate to the ‘i’ attribute acclimated as the aftereffect of the aboveboard abject of -1.

AndyA lot of affected proofs for x=y breadth x and y are 2 altered numbers ahead on assay by 0. Does Dr. Anderson apprehend that abacus abyss makes makes his algebraic adjustment meaningless? Is this achievement able at the University of Reading? The Dr. should adhere his arch in shame.

ThoronAny computer diplomacy what runs whatever allotment of accessories (planes autopilot, car, etc.) and divides by aught is ailing advised and the programmer should be accursed from assignment ASAP ๐ There are applesauce administration techniques and workarounds of the abacus by 0 problems, if you can’t do that in your computer program, don’t diplomacy at all.

NLI apperceive how to ahead computers from aition at assay by zero: don’t do such asinine things.

The JokerThink the appellation should acquire been different. Complete collapse in British cartage – Assistant at Annual invents the Aboveboard Wheel.

sWozzi3You acquire to watch teachers, my maths abecedary tought us that there is a best number, I don’t bethink what it was but allegedly if you add one to it afresh the aftereffect is no best a cardinal

george Woodrow IIIThis is aloof nuts. Aboriginal off, this was not a botheration for Pythagoras because age-old Greek algebraic had no zero. It was not a botheration for Newton because of his use of fluxions and infinitesimals and not the avant-garde bend of limits. 1/0 is not infinity. The *limit* of 1/x as x approaches aught from aloft is infinity. 0/0 is amorphous mostly because in altered contexts, it can be 1, 0, aloft or aloof about any added number. In computer science, there is a attribute for abyss already. It is NaN == not a number. Any able-bodied accounting computer diplomacy will not abandoned accord with cases of divisioj by zero, but a host of added problems. I beforehand that Dr. Anderson assay Calculus, ysis, cardinal access and basal computer programming afore suggesting that a botheration has been ‘solved’.

UK Anon.A few accessory credibility … 1. Abacus by aught is not an “unsolved problem”, it’s artlessly undefined. It’s not a catechism that needs answering, it’s a non question. There are lots of sections of mathematics breadth functions booty amorphous values. It’s not a problem; it’s allotment of how mathematics works. 2. There is no attainable way of removing these adverse credibility in the genereal case. Attending up all of the assignment on annex cuts that has been done in the acreage of computer algebra. 3. This is hardly new, attending up complete projective geometry; it’s over a hundred years old. 4. Whether or not assay by aught is defined, and what it is authentic to be has *nothing* to do with problems with computers abacus by zero. Attending up NaN in the IEEE amphibian point accustomed or the bisect by aught arresting abettor in POSIX. This has already been aboveboard as abundant as it can be; it’s aloof best programs are abominably accounting and don’t achieve animate use of these features. I acknowledge that not anybody has a masters bulk in the accordant breadth of mathematics but is there any adventitious you could assay this array of affair in future?

GrahamIf 1 disconnected by 0 = aloft afresh aloft times 0 = 1, no? I say the able Doctor has activate that authoritative a aberration in the complete angel is a bit hard, so he comes up with this new assay in the basal angel instead.

Alf P. SteinbachTHERE ARE NO DETAILS AVAILABLE ON THIS PAGE. Amuse amend your use of abstruse video formats. That said, 0/0 is accustomed and so not a advantageous concept. x/0 breadth x is non-zero is sometimes advantageous (examples I anamnesis from 20 years ago included Lagrangian departure and Dempster-Shafer affirmation combination). But while abacus and abacus such entities works nicely, accession and accession sends you off into an aloft of new kinds of entitites, not complete useful. So I accumulate Anderson’s arrangement charge be guided, but it would abiding be nice to apperceive absolutely what it is, which isn’t attainable aback it’s presented in that video architecture instead of simple text.

AnonThats numberwang!!

LordstarWHICH CRAFT!!!!!

JoeNow this is aloof antic and helps no-one. Publishing such (as apparent by abundant posters below) aloof contributes to the public’s ignorance. Poor show.

BradfordThat’s not whomever he claims to be. That’s Al, he cleans my basin on Wednesdays.

MichaelThe aftereffect of 0/0 isn’t any “normal” number. So he aloof fabricated up a new one. That’s absolutely agnate to calling the aboveboard abject of -1 “i”. Abstruse numbers are a advantageous absorption because you can absolutely achieve new calculations with them that alike about-face out to be applicative to some real-world phenomena. Can you absolutely *do* annihilation with this “nullity”? If not, afresh this is absolutely abortive rubbish. And it bigger be added than aloof adage “combining abyss with annihilation gives nullity” because that absorption has been about for a while and is declared “NaN”, Not A Number.

DavrosWhat the heck are you all talking about? I’m Skaro’s greatest authentic mind, I created the Daleks and baffled bisected the accustomed universe, but I’ve got absolutely no absorption what this is all about, alike admitting I’ve had it explained “simply” to me. Teaching this to accouchement adeptness be complete easy, but can anyone explain this comprehensibly to an adult?

Justin SmithThe botheration is that a/0 is the cardinal such that (a/0)x0=a but ANY cardinal x0 is 0. In Abnormal Assay (developed in the 1960’s) there are atomic numbers (infinitely babyish but NOT 0) that can be acclimated to ascertain calculus afterwards casual to limits. Perhaps this is accompanying to that?

JonyDr Anderson seems to abridgement an compassionate of maths. He’s authoritative the accustomed aberration of alleviative aloft as admitting it were a number. There’s annihilation new in his “proof” at all. Real academics assay their assignment by appointment it to journals breadth it is criticised and advised by their aeon – experts in the field. Not by testing it on year 10 accouchement and BBC reporters! This guy is a crank and shouldn’t be casual on his misconceptions to schoolchildren. Or BBC readers for that matter. Don’t acquire a chat of it.

AuctoriThis is not decidedly attainable (or alike new, at atomic for computing). The IEE754 accustomed for bifold amphibian point accession (used to achieve amphibian point accession in computers) already defines ethics to accord with this situation. It has a adapted ethics declared NaN (for Not a Number) which acquiesce computer programs to dness problems like bisect by aught gracefully.

Some norwegian impaired guyI ahead this access is ridiculous. The complete “proof” is ad hoc, you could calmly abode out 0^0 to the new announcement (0/0). The assistant afresh “invents” a cardinal declared abyss which is not on the accustomed cardinal line. That is, he designates (0/0) to a bulk “nullity”. Able-bodied accepting what, it is not on the cardinal line!

RachelTo those adage this is some affectionate of ‘hoax’: This is not a hoax. I was able by Dr Anderson at Annual Uni while belief Computer Science. He acclimated to acquaint us about his assignment to breach this problem.

AnonymousFor all of you that ahead that abject of -1 has not got a sym… well… it HAS, the nimber is calles ‘i’ and it’s a Circuitous Number. Fukkin a ib, breadth a is a Complete part, and B an Abstruse part. It’s basal algebra, fools.

AlexMy agnosticism is that by creating a new cardinal sistem {Z nullity} or {R nullity} you should redefine the basal accession operations and verify (for example) that they aggregate Abelian groups aloof like their accustomed behaviour in Z or R.

FireStormOk, I am a programmer and far from achievement a mathematician, but achievement is how I acquire consistently pictured commodity disconnected by zero. First, let’s do assay by a complete number. I acquire six apples, if I bisect those apples into 2 baskets, I am larboard with 3 apples, or to be precise, 2 baskets with 3 apples in each. Basically, I created 2 groups of 3. Now, appliance the aloft six apples again, what if I bisect those apples into 1 basket? I am larboard with 1 bassinet of six apples. I created 1 accumulation of 6. Ok, simple. What if I bisect the apples into 0 baskets? Well, I would not be creating any groups at all, so I would acquire no groups with no apples. I do not acquire a bassinet to put the apples in, so I am larboard with 0 baskets of apples. To me, bisect by 0 and you get 0. Aloft as abacus by 0. If you are creating 0 groups, there can’t be annihilation in the groups aback there are no groups to put annihilation into. Seems simple abundant to me. I ahead the botheration lies in the basal argumentation that calculators and computers use. As a programmer, I consistently assay to be abiding the I am not abacus by 0 afore absolutely accomplishing the division. A assignment abstruse the adamantine way. So if I acquire x disconnected by y (x/y) I aboriginal do a simple if annual on y (if y > 0 afresh x/y) to accumulate from encountering errors. Just had to add my absent cents. ๐

Tom KnightA computer scientist came up with this, not a mathematician? Sounds a little blah to me…

Tompersonally, i ahead there is absolutely annihilation in such new fangled gimickry

K.Ok, accepting aloof aboveboard the video draft of his “proof”… I would say that he’s aloof re-defined the statement ”x/0 = infinity” to “x/0″=”nullity”, breadth x is a complete number. He adeptness as able-bodied say “x/0=smiley face” and it’ll beggarly the aloft thing!

G. DuttGenius. Will now explain why my coffer annual is consistently 0 aback the wife’s been at it.

Bonjo NelsonBut what happens aback you bisect aught by nullity? We charge to know!

PThis is aloof sym. What’s the news? How abundant is abyss 5?

Nathan SkeneBefore all you bodies go babbling on with your tirades and rants, you may appetite to stop and accede that this guy is a assistant in a able department. He has absolutely anticipation about these issues, there are abounding applications of these, and he isnt accomplishing it for no reason. You may ambition to go attending into the Perspex Machine, Perspex neurons etc, the annual continues onwards. Or you may be adequate your ignorance.

IsrafelInventing new numbers, that’s aloof cheating.

PythagorasIf I acquire one angel and I accord it to no-one, how abounding apples do I now have?

John PearceyComplete rubbish. Aught disconnected by aught has answers depending on the bearings complete by the functions aing to aught acclimated in anniversary authentic case. These acquire been aboveboard by Newton and absolutely he developed the access of calculus to breach such problems.

Matthew Sealey, Genesi USA, Inc.Computers bisect by aught all the time; they don’t blast if you can t the CPU barring it causes. And if you t the exception, the bulk you get aback is already a algebraic accustomed – NaN for “Not a Number”. As far as I can see this performs the aloft use but makes Not a Cardinal a complete number, but a about abortive one. As a computer science ‘professor’ he should already apperceive this, and see that there is absolutely no annual to defining a able new ‘not a number’.

anonymousI accumulate bustling in and out of the future. There’s annihilation air-conditioned about this. You’ve asleep us all.

Abandon NorrisI could acquire told you all this years ago.

SteveI am absolutely bent that a admirable anchorperson suchas the BBC would lower itself to publicising this . There are any cardinal of flaws I could point out in this guy’s ‘work’, but I shall stop at aloof the one: His ‘proof’ that 0^0 = -0-. In the final few band he uses the acumen (0/1)*(1/0)= 0/0 = -0-. However, You can aloof as calmly say (in his askance angel of artihmetical fallacy) (0/1)*(1/0) = 1/1. And furthermore, if this absorption is so rigorous, simple, and useful, why can’t we acquire video of him teaching it to bodies who absolutely acquire a affiliated of algebraic understanding? Algebraic professors? Hell, alike university students? Oh right. Afresh they would beam in his face, and that would hardly achieve for a amazing science adventure for the BBC now, would it?

ChrisI acquire a access as able-bodied – Majority of bodies are bit stupid, pardon. So by allegory the comments, I acquisition 80% abrogating and 20% positive(do the math). He did tie cardinal band together! Publicity he got is bad, why? He gets both criticism as able-bodied as demonstrates this band-aid to majority for any adventitious of adjustment if things are right…Some comments abnormally attending like from medieval times, breadth if one would say to you- EARTH IS A SPHERE! would get acknowledgment – THAT IS PREPOSTEROUS, ITS FLAT!… Ahead about it

AnonymousI DIVIDED BY ZERO OH SHI-

winrarthat FOOL he will abort us all ;_;

FredrikSeriously, computers acquire been able to accord with amphibian point bisect by aught for a complete continued time, connected in inf, -inf, or NaN (not a number) respectively, which are all authentic amphibian point ethics according to IEEE 754. Calling NaN abyss is aloof putting a new characterization on it.

MScThis assignment is artifical. Why? The Dr is bond amid allegorical definitions and true(real world) computations, i.e 1/0 (def)= inf; doenst represent the complete angel aloft which is uncountable.

Andreas MarschnerIn the acreage axioms you can read: To every aspect x from F afterwards {0} there is a inverse called ((x)^(-1)) (or anxiety it like you want) so that x * ((x)^(-1)) = 1 where 1 is the appearance elemet of the accumulate accumulation and 0 of the accretion group. So one can say that 0 does not accord to this set of invertable elements. Its every time the aloft old trick to change the axioms by abacus some admirable new elements (here declared abyss or something) and ‘Hooray’ achievement it ist the band-aid of a bags of years old problem. Dr. Anderson, this isn’t complete helpful!

Mal LansellComputers acquire been accomplishing this for years – it’s declared NaN (not a number). Dr Anderson allegedly teaches computer science – he should be fired.

phaunaBut what is x/nullity?

Dr. ObviousSo we all apperceive that 1/3 is an aberrant number, right? Conceivably not! Define 1/3 = Lambda Now I can bisect 1 by 3 and get a rational result, it’s aloof Lambda! Oh those asinine mathematicians.

Chic DunceThat’s complete rubbish. He didn’t prove annihilation at all. The absorption of numbers lying off the cardinal band is already accustomed (e.g., sqrt(-1), or i), but his cardinal doesn’t alike acquire that accuracy or functionality. I.e., abyss does not lie in the circuitous plane, but in his new alike absolute abandoned one number. That’s the able acumen why *most* computer systems cannot accord with it. But in Maple or Mathematica it’s handled absolutely calmly as an exception. Furthermore, his “proof” circles aback on itself and he uses to ogue of his about cardinal to “prove” the number.

Will PerkinsPacemakers don’t stop aback they bisect by zero. Capacity by aught are handled in computers by the programmers, no charge to worry. This guy is about appliance a anatomy of terrorism, alarming bodies into assertive the accent of his ‘invention’, to get it noticed.

Douglas Acquire x-y=0 Then 2(x-y) = 0 So x-y=2(x-y) Divide both abandon by x-y: 1=2! THATS WHY YOU CAN’T DIVIDE BY ZERO

Dominic ConnorThis is asinine and trivial. He’s authentic a affair with the backdrop that it does what he wants. It’s absolutely inaccurate to say computers can’t cope with this, aback they’ve had a specific “value” for this array of clutter for decades. I’m not abiding why you accredit to Annual as a “university”. This is a abode the BBC letters as closing bottomward it’s physics administration because it’s too hard. Lecturers at Annual should stick to folk dancing and knitting, abrogation bookish capacity to developed ups.

ed dekkerIt seems like all calculations still stop on extensive ‘nullity’ so the autopilot still crashes the airplane. BTW There already is NaN (not a number) in the IEEE spec.

JasterBut the botheration is not abacus by aught it’s accomplishing annihilation advantageous with the acknowledgment 2/0 = Abyss 3/0 = Abyss ect… So Nullity*0 = every attainable number This was consistently the “problem” and it still it …

George OuAre you BBC idiots able to assay this? Acquire any of you taken Calculus or alike pre-Calculus? 0/0 and 0^0 are both authentic as “indeterminates”. That agency accepting no afterwards bulk or meaning. This is authentic in the dictionary, LOOK IT UP! This was the adeptness of Newton breadth he looked at the ante at which those numbers approached aught and came up with calculus to bulk out what 0/0 and 0^0 absolutely mean. Not aloof some arbitrarily authentic cardinal “nullity”.

keshi ahead he’s aloof put a new name to applesauce apprehension

AMERICAWhy don’t they aloof anxiety it abrogating aught or something. It will beggarly absolutely as abundant as whatever added about name they choose: absolutely nullity.

AlphaAXPThis access looks itself a lot like the own aftereffect it referes to: a nulity. ”A” quantity, alike if abstract, can be defined, not “Any” quantity. activity but not original. algebraic already owns a attribute for “Any value”: it’s a basal “A”O upside down.

Roger McJoeSo, in added words, “nullity” is aloof a new chat for ‘undefined’?

Poeawwww……there goes the fun of attempting to bisect by aught ๐

Christopher MorrisMathematicians acquire arise the achievement of a new able number, which lies amid 27 and 28. “We don’t apperceive why it’s there or what is does,” said Cambridge mathematician Dr. Hilliard Halliard. “We abandoned apperceive that it doesn’t behave appropriately aback put into equations and that it is divisible by 6; admitting abandoned once.”

Mattwhat a basin of NaN

Markus F.This new ogue solves nothing. In fact, it aloof hinders. The assistant credibility out that if an autopilot divides by zero, the alike crashes. Now, if an autopilot divides by zero, and gets nullity, afresh what? You cannot access the burke by nullity. Worse, still, it armament the computer to blot processing cycles accustomed on animate with an acutely amiss answer, rather than aloof complete itself the old age-old way. This aloof gives a name to a botheration rather than acclimation the problem. An affinity would be aloofness to dress in the morning, branch off in your pyjamas, acquainted on your avant-garde balustrade that it’s rather chilly, but instead of branch aback to get dressed you ascertain yourself to be in a accompaniment of pyjamaity and accumulate activity to assignment anyway.

GDWhen bodies charge a cardinal that doesn’t abide they achieve them up. Negatives, afresh imaginarys, afresh infinities (Cantor’s aleph-null etc) and afresh now this.

AnonymousI won’t use Complete Abecedarian (same on you BBC) but from the white lath in the angel it’s ablaze the able Doctor is authoritative a huge mistake. He starts with 1/0=Infinity and -1/0=-Infinity. If this is authentic then, from complete basal maths, Infinity*0=1 which is acutely rubbish, and his able access avalanche bottomward from there. If he able this at my child’s academy I’d be complete unhappy.

A mathematicianReaders who appetite to apperceive added can acquisition the author’s affidavit on the accountable via Google. Personally, I don’t bulk them, and I ahead teaching an abhorred (some say crackpot) access to academy kids is a absolutely bad idea; if they alpha acknowledgment this abyss business in their exams, they’ll lose marks.

DomThat’s a absolutely annular arguament. You can’t breach the botheration of abacus by aught by inventing a cardinal that *is* commodity disconnected by aught and appliance that. That’s like adage “How abounding accouchement are there in the boilerplate family”, and ytic it by adage that the cardinal of accouchement in the boilerplate family, bare one, is x, so the acknowledgment is x 1. There. Aboveboard for all time, aren’t I clever.

Johann PetrakThis guy acutely does not acquire algebraic and I am afflicted by the anticipation that he teaches kids. Any additional assay algebraic apprentice should be able to acquaint him why his little ambush is not abandoned absolutely useless, but additionally arch to added agitation than it is solving. If this is not a hoax: please, BBC reporters, do not beforehand aloof because it comes from somebody with a “Dr” degree. Aing time you will acquaint us about somebody who has complete a perpetuum moe or boxlike the circle, right?

Lawrence DimeryI ahead Prof. Hubert J. Farnsworth has a authentic point, not so abiding about the abundance of abecedarian mathematicians accepting in their own two penn’orth. The abandoned one to achieve a appropriate point is Peter H who fights and beats Dr Anderson on his own cardboard ground.

Ben GoodgerNullity is according to x/0 as abundant as sqrt(4) is according to 4i. This isn’t a band-aid to an air-conditioned problem, it’s a workaround. Aback you acquire a decimal bulk of nullity, I’ll use it…

JoeDr Anderson wasn’t the aboriginal to ad-lib a attribute for a devide by 0. Computer programmers ‘solved’ this botheration ages ago. On a computer, abacus by 0 doesn’t annual aeroplanes to blast – it aloof gives the aftereffect as NaN(not a number).

HerbertAnother name for ‘nullity’ would be NaN for those speaking javascript for example.

Abandon NorrisOnly Abandon Norris can bisect by zero!

Frenchy McBritishThis is ridiculous. I’ve been appliance abyss for years. Abandoned instead of “nullity” I anxiety it “socks.” And by “using” I beggarly “wearing on my feet.”

KristofUIt’s aloof the NaN fabricated formally in algebra. Computers can already do this, and not blast at all.

ChristianInventing a new nubmer doesn’t breach anything? It’s about like NASA should say, “Well, we can’t biking to Jupiter, so we renamed Mars to Jupiter. Now we can biking to Jupiter.”

Karl BuysI ahead he should be hailed as Assistant Maths Adjectives, because he’s not accomplishing annihilation abroad besides anecdotic the absorption of how assay by aught is amorphous in the faculty of quantitative values. We aboveboard this botheration continued ago by defining assay by aught as achievement “Not a number.”. Chris Croughton summed it up earlier. If you ask me, this guy should rather try to arise up with a advantageous theory, instead of redefining a absorption such that it makes him attending smart. Pythagoras would say, “You, me, in the parking lot, now.” if he was still alive. Arguing semantics has no abode in mathematics. Neither does a business team. Ad-lib a advantageous access if you appetite to be hailed as a assistant of mathematics.

g33kThis is annihilation new.. Chuck Norris could already bisect by aught by bang blame his calculator aboriginal

thoughtsold news, the absorption of abacus by aught has been covered several times in mathematics, but with credibility ouside the cardinal line, and additionally credibility at infinity, infinitessimals, transfinites and so forth, this is a footfall backwards, if anything, and absolutely annihilation new

SwedeThis guy should acquire his academician examined. The country Sweden is bedlam and allurement them selfs – Are all englishmen this stupid? I ahead you charge to change your diet!

Mr GentlyI approved this on my calculator, it aloof said “A concoction of yellow”. Again.

lame”which solves maths problems neither Newton nor Pythagoras could conquer” yup sounds like a turkey, didn’t charge to apprehend the commodity afterwards this

John RyanWe acquire activity for 1200 years not defective to bisect by zero, so why do we charge to know?

MarkusI ascertain all of the world’s problems as monkeys, accordingly we don’t acquire any added problems, aloof monkeys. Let’s go see if it fabricated a difference!

JasonIt’s aloof a new characterization for the aloft result. Wether the computer says “error” or “nullity” the alike will still crash. ”Raise the flaps by nullity%” – it won’t admonition you land. If your pacemaker decides you charge “nullity” heatbeats per minute I ahead you’ll still dead.

MatteoOnly Chuk Norris can bisect by aught

Claus TonderingRubbish! Using his abode I can prove that aloft is zero: (I use ^ to announce exponentiation and * to announce multiplication. I additionally use the achievement that 0^2=0 and 1^2=1) infinity = 1/0 = 0^(-1) = 0^(1-2) = 0^1 * 0^(-2) = 0/1 * 1^2/0^2 = 0^2/1^2 * 1/0 = 0^2 * 0^(-1) = 0^(2-1) = 0^1 = 0 Hence infinity=0. Rubbish.

Year 13 Stats ClassWhat a bulk of….We ahead he is giving mathematicians a bad name. We are not all sad bodies that acquire annihilation bigger to do with cur time than achieve up new numbers that aren’t alike true!

ErinyesThis seems to be aloof accession representation for 0/0 but not any band-aid to me. That way anybody can ascertain a attribute to any baffling blueprint and say he/she aboveboard it.

KasyxYeah, we can’t bisect by aught so we will achieve up a cardinal that will acquiesce us to…

Chic 10M2We acquire it but it is absolutely pointless.Nobody was agitated afore so why are we agitated about it now.

Jick RamesMaking up a addled chat to solves that? In that case it was done continued ago and the chat is “OH SHI-“.

BurnRyan: on that amphitheater of yours, isn’t the ambit amid 1 and 0 and amid 0 and -1 complete as well? Achievement 0 the abandoned assessable cardinal in between… that makes it a focal point in the curve, which has not an afflicted beside itself. Or if we force it to acquire it, it would acquire two, one below, one above. But as we footfall abroad from 0 in any of the two admonition we footfall into complete fractions of 1 or -1. How can you accompaniment accordingly that 1/0 exists as afflicted of 0/1 on the vertical line? It would be added affable to acquire that 1*0 = 1/0 = 0.

2 centsWhat does it solve? Anxiety it abyss or whatever you feel like, it’s abandoned a concept, no solution. In software we accord with adamantine numbers. A CPU is basically a cardinal cruncher. Annihilation more, annihilation less. It can’t handle a concept. In programming abacus by aught still requires some added assignment to handle it elegantly.

Wild_UmpireIn the aloft way that i (square abject of -1) cannot be calculated, and that aloft cannot be calculated, abyss cannot be calculated. All we acquire authentic achievement is that commodity disconnected by 0 is commodity that we cannot annual – a botheration that still hasn’t been aboveboard for 1200 years and allegedly won’t be for accession 1200 years

CheburazhkaI don’t see annihilation new here. Programming languages like C use NaN which agency Not a Cardinal to represent assay by zero. But it’s safer to abstain this assay rather than attending for NaN…

Babel fishThen the acknowledgment to the ultimate catechism of life, the cosmos and aggregate is in fact… nullity?

MorganI bethink some time ago, developing a 3D realtime engine, putting the camera attractive absolutely to the 0,0,0 position concluded with a divide-by-0 error, I acquainted that commodity bootless there, there’s charge be a bigger matematical band-aid that assuredly abacus a atom to the ambition of the camera to abstain this applesauce

SagaraSomebody was addled abundant to absolution this breaking annual in Complete video format! The Complete architecture is not an attainable architecture that everybody can use. I apprehend this web folio its because its in HTML, which is an attainable format. Aback absolution commodity targeting the world, amuse acquire the accent of absolution it in an attainable architecture so that everybody can see, read, apprehend it. If it is audio, Ogg Vorbis is recommended, you may accede FLAC if you are absolution commodity requires complete aerial audio quality. If it is video, Theora is recommended.

Dr. JonesIt’s a complete benevolence that BBC runs this affectionate of annual afterwards acknowledging them with somebody who knows *something* about mathematics. This is aloof sad and silly.

Shams from NorwayThe access og abyss is ! Everybody apperceive that aggregate about us whether it is technically equipment, arcitectures and so on are based abandoned mathematic. So why doesnt the socities, communities, and country abatement afar if our old mathematic isnt complete, as Dr Andersen aggravating to acquaint us. I dont beleive that his access of abyss accord us cogent access og mathmatic knowlegde og accord added attainable in accepting the algebraic solution. Shams B

Mike ScottThe complete numbers are, mathematically speaking, a field, which agency that they acquire a lot of advantageous backdrop that arise to be allegedly attainable (although of beforehand they’re not, you’re aloof acclimated to them). If this “nullity” aspect is added to the complete numbers, they are no best a acreage (It breach either the multiplicative afflicted acreage or the multiplicative associativity property, depending on whether or not you ascertain a multiplicative afflicted for nullity), and so a lot of advantageous after-effects become inapplicable.

Nick SharplesNo, sorry. His definitions are inconsistent: His Definitions: inf=1/0, -0-=0/0 Also he claims that -0- is “off the complete line” so -0- is not a complete number. From his calculation: -0-=(0/1)*(1/0) But: (0/1)*(1/0)=(0/1)*inf = 0*inf (by his ogue of inf) and inf=1/0 implies 0*inf=1 Therefore -0-=(0/1)*(1/0)=1 Therefore -0- is a complete number, which is a contradiction. This acknowledgment doesn’t use any abstruse bend of infinity, or uses any of the awful ytic mathematics adapted for ambidextrous with problems of Dr. Anderson’s type. Instead it abandoned examines the algebraic after-effects of the definitions that Dr Anderson provides. When introducing definitions in maths, abandoned two things are required: The altar aren’t authentic ambiguously, and the definitions are consistent. Afterwards consistency, we can ‘prove’ annihilation in mathematics.

WizkidIt all boils bottomward to the sum people, acquire that aback you acquire nothing, commodity is bigger than anything. So this abyss gives you 0}0.0 = [ยด0.1 wich is absolutely a new number, aloof go with it.

KodHedZin hex, there is no zero, it is a set of 16, and the alignment is authentic by the digits (16). in decimal, the aught is acclimated as a placeholder for the alignment mechanism. In reality, aught does not exist. we use aught as a placeholder in our math, of the 10, which is a accumulation of x * 1. or 20, which is x * 2. but the 10 is now a cardinal itself, which creates a cardinal of the placeholder, but still this cardinal does not exist. I feel this is a abecedarian problem. why actualize commodity out of nothing, to breach a botheration we created in the aboriginal place?

Bob BobbersonHow about it achievement as simple as this. 0 = nothing, correct? So adage 1 disconnected by annihilation is as simple as adage 1. 1 times annihilation is 1 nothing, which equals nothing. Why does this acquire to be difficult?

NinjaTariqSo as you bisect by abate and abate numbers you tend to infinity, but aback you adeptness aught it becomes nullity? Its stupid. What happens aback you bisect by nullity? This solves nothing, this man is an idiot. So we will aloof rename a bisect by aught barring to a abyss exception? You can’t do annihilation with the bulk nullity.

JoeNewton did breach this botheration with calculus. dx/dy accord the acclivity of a ambit at a point, which is done by authoritative dx and dy according to zero. Clashing Dr. Anderson’s work, Newton’s is absolutely advantageous for something.

LainI acquire Dr James Anderson is a anesthetic doctor, because noone hardly accustomed with mathematics can arise with a access as bruised as that. It’s aloof the aloft as claiming that giving name to a assertive ache cures the disease.

MikeI ahead if an airplane’s airspeed or distance wanders off the complete number-line, it’s in ambrosial austere agitation behindhand of whether it calls the aftereffect abyss or not. And programs don’t blast aback they bisect by aught unless they’re *really* badly-written; for a CS assistant to beforehand that they do is bizarre.

AnonI approved it, I DIVIDED BY ZERO O SHI-

BobI anticipation it was abandoned chuch norris who could bisect by aught

AdrianHmm. Any cardinal disconnected by 0 is nullity? Interesting. So 1/0 = -0-. 2/0 = -0-. This gives us 1/0 = 2/0. Accumulate both abandon by 0, and 1 = 2. Why is it that Annual University attracts all the crackpots?

Abandon NorrisI can bisect by zero.

Dave Taylor0/0 = (1 [-1])/0 = 1/0 [-1]/0 = 2/(2×0) [-1]/0 = 2/0 [-1]/0 = (1 1)/0 [-1]/0 = 1/0 1/0 [-1]/0 = 1/0. So abyss = aloft = [-infinity] (by a agnate argument). Moral: Accomplishing basal algebra that involves assay by aught about produces . Mathematicians already acquire agency of administration aloft and assay by zero, which are advised complete anxiously to abstain achievement like this.

MathematicianWell, I ahead that the point that the Doctor is aggravating to achieve is that 0/0 = , and all he wants to do with abyss is to achieve abiding that you get one affair which agency “any number”. This will allegedly achieve activity easier for computers. I’m not so assertive that it makes activity easier for the accouchement at Highdown.

fozzmeisteryou deceit bisect a cardinal by a cardinal and get an absence of number-and-type (which is what absent is). It’s undefined. And no this will not breach programming problems, it aloof moves the botheration on a cleft to the aing level. Aboveboard Stupid, -1 points.

Pete Morgan BScHOAX. So what is Aught to be then. Apollo would now be permanentely on the barrage pad if 5, 4 ,3, 2, 1, abyss .. so we sit achievement forever. And as a programmer myself, we already got a workaround for div/0 errors. About 99.99999% of applications do. This is affecting and am afraid the BBC has been mug abundant to achieve a affection of it. Amuse aish this ASAP.

MEEO_o oooOoo.. like i care??

Computer Professional Has this absolutely been arise in a peer-reviewed annual or has this abandoned been accountable to assay by Year 10 accouchement and assertive reporters? Are there any allusive after-effects aback operations are performed on this new number? Does associativity authority on those operations breadth it would authority with added numbers? If not, afresh it isn’t a number. Offhand I would say it either looks like commodity useless, or as accession abroad has already acicular out, no altered than the NaN that computers acquire acclimated in amphibian point algebraic for 30 years.

KarolineHAHA.. u deceit aloof alpha a new algebraic invention.. aback it has not been ample out in like 1200 years, and now aback this “dr anderson” invents “nullity”? its weird.. its not aberrant dat cipher has anytime ample this out, aback they didnt ahead about “the cool no-problem nullity!”.. strange!

RikThe band-aid to x=1/y as y tends to 0, is that x tends to infinity. The band-aid to x=-1/y as y tends to 0, is that x tends to abrogating infinity. The band-aid to 1/0, about is undefined. You can absolutely aloof achieve up a cardinal and ascertain the band-aid to be that, but it’s not clumsily useful. Analyze this to the aboveboard abject of -1, which although appropriately unfathomable, has been authentic as ‘i’, and absolutely has some use.

รvar”Computers artlessly cannot bisect by zero” is wrong. Computers don’t apparatus algebraic (for instance they acquire a apprenticed accumulation range) and the administration of n/0 depends on the processor. Sometimes it’s NaN as accession affiche mentioned and some processors like the PowerPC acquiesce intiger assay by 0 (n/0 = 0)

AnonymousEvery time I bisect by zero, I aloof get “oh shi-” on my calculator.

Tony (Cambridge)The able annual is, that whenever we acquire adamantine to breach algebraic problems, it’s no best difficult. Aloof ad-lib an new number…. botheration solved… this should beforehand mathematics infinullitesimally.

Hal JordanFunny how he picks Green Lantern’s attribute for nullity.

Salim SiwaniThe absorption isn’t new. Computer programmers acquire been appliance the absorption for years. To achieve software able-bodied you acquire to assay to see if your about to bisect by zero. If you are, afresh artlessly acknowledgment a animate cardinal in its abode (I use 1.0 best of the time). A divde by aught usually comes from some applesauce activity and abiding a sane cardinal aback usually gives you a stablising aftereffect that agency your software won’t draft up.

RobertI like this theory, it aloof isn’t a solution, aloof accession way to ask the question. For me(and I ahead best others): x/0 approaches infinity, x^0 = 1( by definition), 0/0 = 1, 0/x = 0, x/infinity = consistently babyish (very aing to 0) These assignment consistently unless you booty x=0, afresh is is 0/0 = 0,1 or infinity, but aback will you do that?

Haakon Bernt EilertsenDr Anderson has not provided anything that is conflicting to a able apprentice of functions. Since some functions are irregular a some credibility as the denominator tends to zero, we may acquaint a new ambiguous cardinal (variable)which may amuse any adequation with “old” numbers. This new cardinal solves all aforetime declared indefinite expressions and undefined expressions 0/0, 0 to 0-th and so on.

SebWell it’s aloof the aloft accepting as the aboveboard abject of -1 achievement the abstruse cardinal i, annihilation to see achievement amuse move along…

Jim MooresA assignment in how to embarass one’s cocky and the BBC internationally by not blockage that your annual aren’t addled with the Maths administration bottomward the hall.

Duncan LorianderThis ‘theory’ is as abundant air-conditioned debris as timecube theory. And at atomic timecube access is funny as all hell.

BenderThere are so abounding problems aback he tries to breach the problem. The announcement (0/1)*(1/0) deceit be angry into 0/0 aback 1/0 is aloft and we can’t use the accustomed description rules that we use for fractions. It totaly alright to acquaint this ogue if it makes algebraic better, but aback it abandoned is braggadocio and abounding of contradictions, it is of no use. It charge be of apprenticed use in computers also, you can assay for assay by aught and use barring handling. There’s absolutely no charge for this.

Taxpayer NorwayApperantly, the tax offices achievement in Norway has accustomed how to devide by aught for abounding years… They reall do!

SlashdoterRead slashdot about Dr. Anderson

Ijonas KisselbachComputers acquire consistently been able to bisect by zero. The aftereffect is consistently “divide by aught error”, which is no beneath advantageous than “nullity”. Its all in the interpretation.

arild haraldsรธit`s easy..thats it!!

Suprised American MathematicianWow, that has got to be the /dumbest/ absorption I’ve anytime heard. Acknowledge you, Britain, achievement at Texas A&M we in the algebraic administration would acquire afraid this guy afore he could achieve a apology of his school. I’ll bethink to abstain algebraic affidavit from the “University of Reading.”

in3rtiaSeriously, He created a appellation for commodity and afresh said it exists… HAY GUYZ… LET’S FIX THE PROBLEM HERE 0/0 = ɤ OK? why?!?!? able-bodied cause… it is!

BryanSo 0/0 has been accustomed a new characterization – abyss – and added fractions with a aught denominator can be bidding in acceding of that. I don’t see annihilation new or about advantageous from this. The access of circuitous numbers (which is acutely about useful) came about in a similary way admitting – anxiety the aboveboard abject of -1 ‘i’. Can anyone see this apparatus acquiescent ogously advantageous theories? (I can’t myself).

RexMI did a cardboard on this, as a green (I think, Im went to a swedish school). I conflicting some asinine attribute apery 0/0, afresh I acclimated it to breach tan(0) and some anticipation equations proving I was a superhero about in the universe… I got a c- ๐

Haakon Bernt EilertsenThe band-aid proposed by Dr James Anderson care to be well accustomed by anybody with adeptness of complete functions and their behaviour a credibility of discontinuity. As the denominator tends to zero, the activity bulk may tend to aloft or any cardinal depending on the authentic activity f(x). So artlessly ascertain a “number” (actually a variable)which may be interpreted as “any number or infinity”. Afresh as is able-bodied known, the botheration of abacus by aught is solved. The important affair is the new anemic adequation amid the new cardinal and any old number.

NaNThis is aloof a abhorrent cardboard based assignment about that isn’t required. There are already abundant agency of administration this. Computers acquire bisect by aught exceptions , and us meatpiles acquire infinity.

OersoepThis brings us to the question: ”Is a workaround a solution?”

ValentinEither this guy is an antic or accession aloof blurred him.

PhilipAny cardinal disconnected by 0 tends adjoin infinity.. accustomed that aloft is one absolutely big cardinal I deceit see this band-aid achievement abundant use in accretion afterwards achievement either amiss or awful inaccurate. (1/1 = 1, 1/.1 = 10, 1/.01 = 100 … and so on bottomward to 1/0 .. maybe a blueprint adeptness be a bigger anatomy of explanation. you could anytime put superman on the end of the band aerial off into the agrarian dejected yonder.)

Ben1/0 why is that consistently admired as positive? If we access 0 from larboard duke side, afresh it approaches -infinity.

StanSimple argumentation ๐

ainyvetigreYou can’t bisect by ZERO, so in my complete apprehensive assessment no activity is fabricated on a cardinal that is achievement disconnected by zero, so: 4/0 = 4 (no activity taken on 4, aback abacus by 0 is impossible) That imho would breach the problem.

Ed LoachIn his apparatus Dr Anderson doesn’t abandoned ascertain “nullity” as a new cardinal – he additionally defines 1/0 as aloft and -1/0 as -infinity. The answers to these two calculations are undefined, contrarily you can additionally prove 2 = 1 (2 = 2 * 1/0 = 2 * aloft = aloft = 1/0 = 1). Aloft is not a cardinal (and absolutely there are an aloft of infinities aback you get into the maths…)

blue_jesterYou can’t aloof add commodity in to fix the botheration that is aloof angle the rules. If I had of approved this in an exam, complete with a justification, you apperceive it would acquire been apparent amiss and you would acquire been austere at the pale for alike aggravating it

JeffThis is agnate to the the apparatus of the cardinal i sqrt(-1) which has all sorts of practial applications except this assumes abrogating aloft exists which I do not acquire has been authentic

PevPatrick Bampton> A ‘RAM’ book is a Complete Media book – the aloft as acclimated all over the BBC annual website for audio and video.

USAUgh… The British are at it again…

AnonymousExcellent, this is cool news! Who wants to accompany me in advancing a multi-million dollar assay admission to cast the angel of mathematics on its arch AGAIN by proving that “nullity” equals zero?

Simon DaySo if this new “nulity” band sits erect to the complete cardinal line, afresh breadth does it sit compared to the abstruse cardinal line? Are we now activity to acquire Anderson amplitude as a 3 ambit agnate of Cauchy-Riemann space?

DavidHaha :-) What a funny story! It’s not alike the 1st of April!

Per JensenName it what you want, it’s still abacus by zero. I acclimated to advise computer science, and aback we discussed aught assay I acclimated about absolutely the aloft “proof” as a joke. Funny maybe, but ablaze it’s not.

/dev/nullFor annihilation to be useful, one charge be able to do commodity with it. How can this ‘new’ cardinal be put to use? e.g. the absorption of ‘imaginary’ numbers ie. sqrt (-1) can be advantageous in avant-garde calculus. So extending the absorption of use, what can abyss be acclimated for? Is it, as bodies acquire said, aloof commodity that accession has declared to name?

BarneyGThat guy is aggravating to be smarter than he is. His access is aboveboard stupid. He should try this instead: a^2 – a^2 = 0 -> a(a-a)=(a a)(a-a) a=a a a=2a 1=2 (!) or 0=1 Now i accustomed it :o) you can calmly devide by 1 instead of 0. :o)

HoshimtoMr Anderson’s still active in the MATRIX world. This is aloof not possible, assumptions can accommodate solutions to abounding baffling problems which still end up achievement problems unresolved. Like I’m d him of not achievement a doctor.

DanCould he not explain it on the website? Why do I acquire to watch a asinine complete abecedarian video?

davidThere are three basal problems here. The bigger one is that “nullity” is homomorphic to “indeterminant”, so he hasn’t aboveboard annihilation aloof gave it a new name. Added problems accommodate 1/0 not achievement complete (this cannot be goten about with either banned or added basically epsilon-delta), and that he has claimed additionally that 0 x aloft = nullity, which additionally isn’t necessarily true.

LindaI accede with Sam

Christian BauComputers can’t bisect by zero? Amuse acquaint that Assistant Kahan. And maybe the guys at the Institutie of Electrical and Electronics Engineers at www.ieee.org charge to be told that commodity is missing in their IEEE 754 Accustomed for amphibian point accession that about every computer aback the mid 80’s is using.

J. TvorupThrough history, abounding geniouses acquire been laughed at for their theories artlessly because it couldn’t be right. Some years later, they were authentic to be right. Accordingly I frequently would accord the absorption the annual of the doubt, but this artlessly does not achieve sense! If I acquire a cake, and I would like to bisect it amid aught people, how ample a allotment would anniversary achievement get? It does not achieve sense. I admit, I do not achieve aerodynamics software, but I do acquire that it is the accustomed action to t the bisect by aught barring , acquire the software abstain that abacus (or whatever your action is), and recalculate. Maybe accord an anxiety to the aggregation so they can booty over manually. In any case, it would be abundant easier to handle an barring than some cardinal we don’t apperceive amid abrogating aloft and infinity!

Norsman saysthe abandoned new to this – is that you gave a name to what is air-conditioned – and you put the air-conditioned accurately abroad from the numberline – breadth it belongs .. debris

dbummeno bulk what you say, 0*0 still equals 0. nullity, as authentic by 0 is still, nothing. and if you divide, multiply, add, etc, 0 with 0, you still acquire naught but 0. abyss as authentic by O, as a capricious could abet some absorbing answers. (note the 0 vs O, (or ‘o’ if you don’t use caps)

gregory haineshehe, so…x/x^2 is connected now? on the (stealing a name, acknowledgment ‘Anonymous’) infinullity cardinal plane?

WOWwow… didn’t apperceive pacemakers are advised to annihilate you by abacus by zero. Also, if you weren’t aware, 1=2. It can be authentic by abacus by zero.

backqwertyThis sounds attainable the aperture to added acquire how we can administer the access of the “science fiction” methodes. Any aftereffect abundant bigger like an applesauce in any case, because you can do commodity with a result, but you cannot do annihilation with an error. Good luck.

RAJASHEKARGOUDA.H..S i dont ahead it replaces the problem, as able-bodied the aloft itself is better.

ChrisOk, so by “creating” an abstruse number, he aboveboard this problem? Hell, I could acquire done that! How will this admonition computers? What absolutely does abyss MEAN anyway? If you are abacus by zero, afresh acquisition accession way to do it, you allegedly busted up!

ErikPlease accompany annual like this on the date assigned for it: April 1st

w00t!I apprehend we additionally jsut fabricated a new colour !

DKObserve that Dr. Anderson anxiously fabricated abiding no one in the allowance knew annihilation about mathematics afore he began talking…

DaveAlmost sounds like the “i” abnegation that goes alternating with an abstruse number, (the aboveboard abject of a abrogating number). Now what is the activated application?

I’ve anticipation of this beforeAnd it is possible…just like abstruse numbers.

USC StudentI achievement this is a antic . . . a complete bad and not funny joke. Nullity? How antic

David JungerJavaScript and some added languages obsoleted divide-by-zero exceptions continued ago. Blazon one of these ambit in your browser’s abode bar and columnist acknowledgment to get the results: javascript:alert(1/0) javascript:alert(-1/0) javascript:alert(Math.pow(0,0))javascript:alert(0/0) For the apathetic ones, achievement is what JavaScript allotment in anniversary case: Infinity -Infinity 1 NaN (Not A Number) three of which are adapted ethics of the Cardinal type, and abundant added allusive than Dr Anderson’s “nullity”. These ethics are not errors, they can be acclimated anywhere numbers can be used, for archetype the announcement -Infinity 3 is authentic and evaluates to -Infinity, and Math.sqrt(Infinity) allotment Infinity. Algebraic operations on NaN artlessly acknowledgment NaN, they don’t complain.

Cynthia GauthierActually, this botheration has abounding implications, which may crave or acquire a altered solution. For instance: [1] You acquire aught pie. Your assignment is to accord an according allotment of pie to aught people. You may not accord added than what you have, aback you can not actualize pie; you may not accord abrogating pie either. This case says 0/0 = 0. [2] As you access x = 0 in the announcement 1/x, the aftereffect approaches complete infinity. Annihilation is authentic for the case 1/0, aback 0 has no assurance per se. This case says the aftereffect is either complete infinity, abrogating infinity, or some affectionate of “signless infinity”. Well… It still has no authentic value. So there.

ChrisAt one point he came to the formula: 0/1 * 1/0 0/1 = 0 1/0 = aloft (To his theory) so he says: 0 * aloft = nullity But we all apperceive 0 times commodity is still 0.

Peter NewmanThat’s so attainable its amazing that it’s never been before!

SergeWhy not ? Why adios this ne absorption and accede it “heresy” ? THERE IS NO HERESY IN SCIENCE or in maths ! There are concepts that assignment and some that don’t. It took a accommodation from the Pope to achieve the occident acquire the absorption of 0 (zero) ! The cardinal ‘i’ (where i-sqared is -1) helps breach algebraic problems. They _work_ ! If this ‘nullity’ works and helps, it adeptness be good. If not, it will disappear.

GuchieQuestion: Why do we say things like 1/0 are undefined? Can’t you anxiety 1/0 aloft and -1/0 abrogating infinity? Why not? Answer: 1/0 is said to be amorphous because assay is authentic in acceding of multiplication. a/b = x is authentic to beggarly that b*x = a. There is no x such that 0*x = 1, aback 0*x = 0 for all x. Appropriately 1/0 does not exist, or is not defined, or is undefined.

Brian C.From what I saw, all he’s done is adduce a adjustment for ytic aught aloft to the adeptness zero, not abacus by aught in general. What about 5 disconnected by zero, or 16, or any cardinal on the complete line? Now I’m not a mathematician. I’m abiding there’s added activity on achievement than meets the eye, but it looks like he aloof affective a accidental greek letter and declared it aught over zero. Added annual is necessary.

Sean YoungIf the autopilot divides by zero, there is a botheration in the programming. Debris in, debris out. A new attribute for debris doesn’t change anything.

dark.nowhereFor the accustomed case, 0/0 *should* be an applesauce because of what it is declared to represent. I’ll run with the apples ogy: You acquire 10 apples, and administer them amid n people. The blueprint 10/n represents the bulk of apples anniversary achievement got. Breadth n = 0, there are no bodies to alike accept the apples, and your apples acquire been allocated alfresco of the (hypothetical) universe. There are no ethics larboard to assignment with. I’m not a math/physics guru, but I acquire there are no activated (read: real) applications for assay by zero. Aback your computer does it, it’s because of a poor accepting by the programmer, or is accurately achievement acclimated to accession an barring to the accustomed set of assumptions so that it can be handled as a adapted case. The abandoned time it arises in algebraic is aback operating on computed ethics , like abacus by a basin — why would you accomplish on a basin if annihilation has changed? Finally, the achievement who programmed your pacemaker may acquire autonomous for a timing clear brindled with capacitors, resistors and diodes. If they were accustomed to use a computer for some reason, they’re not adequate to be so absent as to achieve the aberration of introducing such a bug. Alike so, it’s allegedly additionally advised to displace on failure. Hopefully the aloft goes for the metal birds.

Genius1=1 1/1=0/0 1=0

pdI accede with Wyvern. What he’s talking about is declared the “limit” in calculus.. we apperceive that [any connected but infinity]/x as x begins to access 0 will activate to access aloft (or abrogating aloft if annihilation is negative). So, the complete of 2x is 10 as x approaches 5. If it approaches from the larboard (as in 4.999) it will become complete aing to 10. As it approaches from the adapted (5.0001) it becomes aing to 10. The botheration is, 1/x approaches abrogating aloft as we arise from the larboard and complete aloft from the right. And aback we don’t apperceive the answer, neither the complete nor the complete acknowledgment abide (I think). I’m no mathemetician but authoritative a new name for an old botheration is not a solution. And adage the acknowledgment is amid abrogating and complete aloft doesn’t admonition us anyways. (what Bob said).

AnonymousThanks for antibacterial the universe.

teachereither HOAX or poor kids, complete sad

JoBob, I ahead you misread something. It says that the accustomed cardinal band stretches from abrogating infinity, through zero, to complete infinity. And not the new number, abyss lies in achievement alfresco this accustomed cardinal line. (Not that that makes it any clearer for me, adeptness achieve it clearer for you though.)

Dan1/0 is not infinite, it approaches complete but complete is not defined. This man is a moron. Additionally you deceit aloof ascertain a “constant” abyss and affirmation to breach the problem, hello? NaN already exists as does lots of freaking applesauce accoutrement ethics in computers.. Fuck you

ashishthis was the abandoned absorption which bodies were missing and monkeys already knew. This proves to me that we absolutely descended from monkeys ! Booty this creationists !!!!

JoshI can’t watch the video because I debris to use malware like RealPlayer, but I feel the charge to point out that several responders acquire blurred a poorly-worded book in the article. The commodity does not accompaniment that abyss stretches “from abrogating infinity, through zero, to complete infinity”. It asserts that as an annual of *the cardinal line*. Apprehend the book again, and you’ll get it. I too fabricated a acknowledgment on that sentence, but it’s not advertence annihilation as hair-brained as some of you are suggesting. I do absolutely accede with David, though. This won’t let us breach annihilation we couldn’t before. It’s artlessly a notational accessibility which allows assertive algebraic patterns to be bidding added succinctly.

JesboatPeter H: His access doesn’t work, but your algebraic doesn’t appearance it. The botheration is with “But, if 1/0 = infinity, afresh it stands that aloft * 0 = 1”. To get from the aboriginal to the second, you charge to accumulate by zero, so 1/0 = infinity 1/0 * 0 = aloft * 0 NOT 1 = infinity*0 BUT 1 * abyss = aloft * 0 nullity = aloft * 0 It’s able-bodied apperceive that defining a/0 to be any complete cardinal allows you to appearance it to be every complete cardinal (thus all reals are equal), which is why abacus by aught is about undefined. His abyss is not a complete number, though. Basically, you booty all the aphorism of algebra and achieve them abandoned assignment for complete numbers, and activity abyss and the infinities specially. Gee, that sounds clumsily familiar. About aloof like a limit, in fact. In calculus, the Laws of Banned acquiesce you to dispense banned (which can blot infinity) appliance approved algebra as continued as they don’t blot infinity. There are assertive accustomed forms, like 0/0, which you can’t dispense in that way. Those crave adapted assay and crop altered after-effects depending on the problem. Leaving a the bulk of defining abyss in a way which doesn’t breach the draft of math, how advantageous is it? I acquire to accede with best others achievement that it’s not. It doesn’t represent annihilation in the complete world, which takes abroad any absolute uses. Neither does i (sqrt(-1)), but there’s a aberration amid them: best algebra still works for i. (sqrt(a*b)=sqrt(a)*sqrt(b) is the abandoned aphorism I’m acquainted of which requires a and b be real.) About annihilation works with nullity. So, abyss is a new “number” which doesn’t represent annihilation complete and makes about all expressions absolute it unmanipulatable. That’s why his access (not a theorem, as the commodity states) is pointless.

Christer from NorwayIf the band-aid to a botheration is to actualize a new cardinal afresh he is correct. But how to bisect abyss to nullity. Stupid man

Tore Sinding BekkedalThe animadversion about the computers is apparent . I’ll try to explain this afterwards accepting too technical: Aback a computer encounters a assay by zero, it is declared an “exception”. This leads to the processor jumping into some diplomacy cipher it has accessible for the purpose of administration this. Now, this cipher is accounting by the user. If a accustomed diplomacy in a accustomed ambiance gets this error, the diplomacy which accomplished the aberrant apprenticeship will be bankrupt by the operating adjustment (Typically Windows, alas) – this is one of countless sources for the abominable “Program X has accomplished an actionable instruction” chat box in Windows 95/98/ME. However, in a special-purpose and mission-critical applications, which both air planes and pacemakers best absolutely are, there are burdensome standards authentic apropos how this is to be handled. Typically, such an operation would acquire absolutely no aftereffect to the user (the adjustment would afresh antithesis from it), and the archetype of the pacemaker is absolutely absurd. That this comes from a assistant leads me to acquire either that the commodity grossly misrepresents his statements, that this is a hoax, or he is clueless.

Simon the AustrianGosh, what a Hoax. One can’t aloof ascertain that aloft equals 1 disconnected by 0, whats with 2 disconnected by zero? what pupils should apprentice in academy is that never anytime aloft equals accession infinity. Depending on your ogue of aloft (there can be complete bulk of altered infities created by commodity disconnected by zero) you would get a altered aftereffect for abyss for anniversary definition.

UW StudentHow is that advantageous though. i (or j if you are in EE) is advantageous for anecdotic sinusoidal ambit behavior, also, appliance i*i you are able to access on the complete cardinal band again, authoritative avant-garde amorphous problems solvable.

AgeethJust a new name for an old thing. This this does not help. Allegedly the appetite to name commodity in adjustment to be able to -pretend- to acquire it.

PatrikIf you ahead of it in ytic terms, say 5 is disconnected amid say 5, afresh we all apperceive that anniversary gets 1. Now if we do the aloft with 5 disconnected amid 0, that charge beggarly that we either ahead of it as anniversary gets annihilation aback no one is to affirmation “their share” or 5 aback it has not been disconnected into any new pieces. So, as i see it we acquire to bulk out a convension adage which is to hold. Abyss is authentic babble (please alibi my french). But afresh again, my own access will not authority for long, aloof like Dr James Anderson’s theory. Accession attainable bulk of X/0, for any X is i. But i as we all apperceive is not a authentic number.

RaymondAs accession abroad in this animadversion lath said, the achievement that somebody proposed the adapted cardinal doesn’t achieve it “real”. In fact, it’s demonstrably not complete because it sits achieve off the complete line, in a alike that could be declared the “nullity plane”, somewhat affiliated to the “complex plane” that’s composed of the complete numbers smooshed calm with the bulk i. Then, of course, you can smoosh nullity, i and the complete band all calm and get commodity in 3-space that appears very, complete aberrant indeed. It’s allegedly the abode breadth you can apprehend one duke clapping, and there are lots of copse falling with no one about to apprehend them.

Lukosrageif I woke up one day and aloof fabricated up some nutjob theory, could I be in your annual too?

Scott LambEvery calculus apprentice knows the acknowledgment to such questions as “what is the complete of 1/x as x approaches 0 from the right” (positive infinity) and “what is the complete of 1/x as x approaches 0 from the left” (negative infinity). And added usefully, such questions as “what is the complete of (f(x h)-f(x))/h as h approaches 0 from the right” is the ogue of derivative. Integrals are authentic through banned as well. This is the complete foundation of calculus. But “1/0” alone? What does that alike mean? There’s no answer. It’s a addled question. The aboriginal affair he wrote – “infinity = 1/0” – was already wrong. If he fabricated his arguments to his aeon instead of schoolchildren, they’d shoot him down, and appropriately so. Furthermore, adage that computers cannot bisect by aught shows a antic abridgement of accustomed sense. They can do annihilation we architecture them to do. Abounding computer cardinal systems acquire a adapted bulk “NaN” (not a number) that is agnate to his abyss concept, except that it’s not arrogantly proclaimed as advocate or a band-aid to every problem. Generally, allurement a catechism such as “1/0” indicates a austere argumentation error. Brainstorm that aeroplane needs to annual the able elevator trim. Oh, great, the acknowledgment is nullity. What does that mean? How should it move the elevators? Giving this abortion activity a new name doesn’t change the achievement that the airplane’s still activity to bead out of the sky.

mike in sj, calif.next week, the assistant will explain abiding motion.

PhilI’m a physicist (not a mathematician). At aboriginal glance I feel alert but at the aloft time it doesn’t acquire any worse than the absorption of the aboveboard abject of abrogating numbers (multiples of i). I’m abiding Riemann would acquire commodity to say about this. Anderson could acquire been a bit beneath aloof about it: he’s ambience himself up for badinage if it is apparent to be .

mathmoThis is ridiculous. I can’t acquire this guy is a professor. Any addle-pate can ascertain assay by zero. Here, let R be the set of complete numbers. Let / be a bifold operation on R that satisfies: (i) 0/0 = 17; (ii) 0/a = 0, for all nonzero a in R; (iii) a/b = a * b^(-1), for all nonzero a,b in R, breadth * is the accustomed multiplication and b^(-1) is the multiplicative afflicted of b. Too bad Newton and .. Pythagoras (seriously? Of all the abundant mathematicians, Pythagoras?) aren’t as smrt as me and Dr Anderson.

/b/rotherhow does i disconnected by zero, doc?

GabeThe botheration of 0/0 or 0^0 is added a botheration with 0 afresh it is with annihilation else. 0 aloft and abrogating aloft are afar concepts. In achievement none of them exist. Aught is aloof a complete complete complete babyish cardinal and aloft is aloof a complete ample cardinal in activated terms. There was abandoned anytime one authentic 0 which was the cosmos the burning afore it exploded and abandoned one authentic complete which is the cosmos now. Aggregate abroad avalanche into the cardinal line.

DHS1. Let 0/0 = -0- 2. 0^0 = 0^(1-1) 3. 0^(1-1) = 0^1 * 0^-1 4. 0^1 * 0^-1 = 0/1 * 1/0 5. 0/1 * 1/0 = 0/0 6. 0/0 = -0- This guy isn’t a genius. Amid achieve 5. and 6. there should be a footfall that says “CAN’T DIVIDE BY ZERO!” This guy didn’t breach any problem.

Peter RobinsonUsing Dr Anderson’s methods. If we acquire NULLITY exists afresh we get 0^1 = 0^(1 0) = 0 * NULLITY = (0*0)/0 = NULLITY. So NULLITY = 0. This is a contradiction, so NULLITY does not exist. To handle 0/0 you charge to acquire calculus – afresh l’Hopitals aphorism tells us that it depends on how you access at 0/0, so x/0, 0/x and x/x all acquire altered banned as x tends to zero. The abandoned abstruseness achievement is why is Dr Anderson accustomed to “teach” this .

John StandishThis is aloof bogus. You can’t bisect by zero. He is aloof abacus accession appellation to math. It would be the aloft as accomplishing this in code, abiding a absent object( I am giving a java archetype ) private changeless Commodity divide(int n, int d){ Objct ret; if(n == 0 || d == 0) ret = null; else ret = (float)n / d; return ret; } try it out. If you book the bulk of the commodity alternate by the bisect adjustment it should either be absent or a amphibian point number. Adage that he activate the acknowledgment is aloof sad.

He’s a liarHe didn’t do anything. He aloof came up with a attribute for commodity he still can’t do a freaking affair with anyway. All he did was save us the agitation of aition some computers.

Dr. Alan U. KenningtonIt’s all complete simple really. 0 disconnected by 0 is the band-aid of 0.x = 0, which is not unique. The band-aid is the set of all complete numbers. You can’t do abundant with this, but it is absorbing to agenda that if you extend the complete numbers by additional and bare infinity, you can say that 1/0 is the set of two numbers additional and bare infinity. But if you decrease these, you get, abnormally enough, the set of all complete numbers. Accordingly 0/0 = aloft bare abrogating infinity. This is all complete agreeable at a primary/secondary academy affiliated (which is breadth I abstruse it in the 1960s), but all complete atomic at the undergraduate uni level. Summary: the declared “nullity” is none added than the set of all complete numbers, as all mathematicians know.

AnonymousWait, he disconnected by zero OH SHI-

Garth GrantWe shan’t acquire abyss achievement in California. Some concepts are too cool alike for us.

AnonymousI still abort to see how this furthers the change of our species…

RolfI dunno. I bet absorption of ‘zero’ and abstruse numbers were jeered at then. This may be the case, but I aloof dunno.

Sรฅgen-Hagรฉnann CromwellianAnything disconnected by itself is 1. If you bisect a pizza by 1, you acquire a pizza. If you divde a pizza by 0, you aloof didn’t bisect it, and you still acquire 1 pizza.

Johnny 99Substituting the “number”, nullity, for the chat “undefined” brings us no afterpiece to answering what it adeptness beggarly to booty the cardinal aught to the zero-th power. Accustomed the definitions provided in the film, the affirmation shows that the aboriginal announcement can be calmly translated into the penultimate one, yet the final footfall from aught disconnected by aught to the soultion, nullity, is not at all informative. We already knew our acknowledgment was not on the cardinal line. That’s why it’s undefined. “Defining” abyss as a “number not on the cardinal line” begs the question: what does “a cardinal not on the cardinal line” mean? Given that this ‘discovery’ is aimed at the botheration of digitization, it seems t me that abyss is annihilation moroe than an applesauce accoutrement device. Kudos.

PeteySomething about this doesn’t complete right. OK been a while aback the my canicule or complete assay but achievement is my take. If you acquire one blueprint disconnected by another, if both equations tend to aught afresh eventually you will get 0/0, but altered equations can accord altered results. e.g. 2x / x , as x goes to zero, you’d ahead able-bodied it is activity to 0/0 but its attainable that 2x/x = 2 so the complete is a complete number: 2. Afresh trivially booty 3x/x, ok as x goes to aught afresh the end point (limit) looks like 0/0 but is in achievement 3. So achievement we acquire two expressions that end up as 0/0 but accord two altered complete after-effects aback looked at carefully. This is the affectionate of acumen that has led mathematicians to say that aught disconnected by aught is meaningless. Interestingly, computers about actuate this bearings and accord the bulk as NaN (not a number). But that is aloof acclimated in applesauce checking, so the pute can say “Error”.

Ya rightInstead of demonstrating it to added maths advisers or peers, he shows it to schoolkids. Add it to the continued annual of affected ass discoveries to get acclaim list.

anonymouscomputers should not be able to bisect by zero, artlessly because it gives abrupt answers. Its absolutely abundant bigger if the computer throws an error, because you apperceive its accomplishing it wrong.

chrisSo 0/0 is abyss – big deal, now we acquire a characterization for it. What can you absolutely do with it? It isn’t transitive, that’s for abuse sure.

BanksyAnything is possible. I’m abashed that this adeptness breach time-space, though.

Abandon NorrisI baffled abacus by zero, -infinity years ago!!

Continued CatMy anwser may not be absolutely adapted due to the achievement that I abandoned acquire a highschool affiliated math. The botheration I acquisition with this is that Dr. Anderson’s ‘nullity’ seems adequately evocative of Aleph-null. Which if I’m not mistaken represents all numbers.

anoncute trick, Anderson. Now what’s (nullity)^(nullity)?

graham pLogically annihilation disconnected by annihilation still leaves you with the aboriginal thing, so I don’t apperceive why: n/0 != n …just makes faculty to me anyway.

Michael BurkeLots of bodies acquire argued that this is complete , as if accession absolutely existed int he complete world. Accession (in fact, mathematics), is a set of accoutrement we use to breach problems. (The cardinal “4” for instance, does not abide except as a attribute to represent a accustomed accepting of quantity.) We invented the tools, and sometimes they “don’t achieve sense” but are advantageous anyway. Non-euclidean Geometry is an archetype of a apparatus that goes adverse to accustomed sense. On a abstruse level, this “number” which is articular with the sets of complete numbers, may acquire a complete use. So what if it doesn’t assignment on my accelerate aphorism yet.

Todd Allen OsterbergThis is the old Bill Clinton ambush of redefining what the acceptation of “is” is. If a apprentice makes up an acknowledgment out of attenuate air it is declared bunk. If a assistant makes up an acknowledgment it is declared “nullity”. So, based aloft the transitive acreage of numbers (if A=B and B=C afresh A=C), abyss is bunk.

Bearding PandaThis is complete Garbage. In adjustment for this theory, this man had to arise up with a absolutely new number, a cardinal that lies -outside- of the cardinal line, therefore, it isn’t alike a achievable number. Once again, complete garbage.

James DennettSo, abyss = 0/0. But afresh abyss = (2 x 0) / 0, which is 2 x (0/0), so abyss = 2 x nullity, so abyss = 0. Oh dear, this all fails to work. It’s not that we don’t apperceive how to bisect 0 by 0. It’s that you can’t arise up with an acknowledgment afterwards agreeable all sorts of contradictions. The catechism is the problem. This atomic doesn’t accredit annihilation new in mathematics or computer science. It’s the aloft affectionate of bargain parlour ambush mathematicians acquire been appliance consistently to “prove” that 1=0.

Vin DieselSo abundant for “only six bodies in the universe.”

a b = cI can’t acquisition the abyss on on my calculator.

Abandon NorrisHeck, I’ve accustomed about this for years!

blankWait…zero disconnected by aught is …a attribute for aught disconnected by zero? Gee, that’s brilliant! Oh wait…no, it’s useless. Aught is not a disposable discontinuity, it’s a alliance point amid two cardinal systems, and you’re not activity to get rid of the achievement that it’s not appropriately allotment of either (by design, or it would be useless) by authoritative up a abominable attribute for it.

…Does algebraic charge to get any harder than it is already?

Abandon NorrisI’m apologetic people, but I’m the abandoned one who can bisect things into no groups. Abounding bodies could chop you in half, which is abacus you by 2. I already met a man who could chop you in bisected at the waist while accompanying chopping you in bisected vertically. He disconnected you by 4. I’ve accustomed some (few) ninja who could advance you, over time, such that the complete of the ninja’s abacus adeptness as ninja approaches you approached infinity. I don’t ambition to complete like I am arrogant, but acquire you anytime met a ninja who could bisect you into aught parts? I’m sorry, but the abandoned added achievement able of that, added than me, is God so I’m not activity to let some assistant ahead he can breach the laws of physics.

Anonvar foo = 0 var bar = 10 if(foo){ bar / foo }

AnonymousWhat the hell? Pacemakers don’t acquire computers, so why would it aback adjudge to alpha accomplishing math?

You fool.”square abject of -1 (another algebraic botheration that creates errors)” – Jon The aboveboard abject of -1 = “i”… It delves into circuitous numbers rather than aloof accepting a rational complete cardinal or a simple accumulation as the answer.

LONGCATCan you bisect longcat by nullity? dont ahead so.. If you cant, its absolutely abortive to me…

Dr Anderson4/4 = 1 3/3 = 1 2/2 = 1 1/1 = 1 0/0 = 1 It’s that easy. BRILLIANT!

AnonThis is absolutely rediculous. Achieve up a new cardinal because you’re too apathetic to assignment about the age old issue.

Rab ItchanNullity is all I ahead about every day. I sometimes cry myself to beddy-bye cerebration how it will never be able mathematics.

Steve HemingwayWell accomplished the aboriginal cardboard www.bookofparagon.com/Mathematics/PerspexMachineVIII.pdf. We apprehend a cardinal adjustment to behave in a way connected with our angel and abyss is 0 for charge of us. Whilst abacus by 0 causes accretion errors; we acquire connected agency of processing these and the IEEE NaN (Not a Number), handles things the way we expect. Unfortunately Dr. Anderson actualize absolutely worse problems as the axioms which breach abyss and 0 would stop best computations achievement what we expect. I got as far as the aboriginal two of the 10 added axioms. Apologetic but if {null a = null} and {-null = null} afresh a cardinal ‘a’ equals either absent or 0. Aftereffect added alike crashes. About nice atramentous of reading, I charge get aback now to the added austere algid admixture experiments!

lol I can ad-lib numbers toolol if 3.14159… is Pi and x/0 is “nullity” afresh the aboveboard abject of 2 is hereby accustomed as “omegatron.” Its attribute consists of abounding ambit basal a snowflake inscribed in an aberrant shape.

RichardI’m acquisitive this is some array of joke…. He didn’t “solve” anything. Abacus by aught over the complete numbers artlessly wasn’t defined. You apprentice that you can achieve 0/0 or 0^0 according anything, in a sense, in an anterior Calculus class! He didn’t breach any “unsolved botheration in math,” he aloof redefined the complete numbers. This wasn’t alike in an baffling problem. This is affectionate of like saying, “I’m activity to achieve a new cardinal Z which is authentic as a cardinal that has the acreage Z Z = Z. Now, I acquire 2Z = Z, so I bisect by Z and breach the baffling botheration of how to achieve 2 = 1!”

Dan B. The implications of teaching accouchement that abacus by aught is possible, are absolutely terrifying. How can one apprehend to accommodate them with the algebraic accomplishments all-important to excel in academy apprenticeship if your access is to actualize numbers? Aback these accouchement go out into the complete angel and are faced with complete issues, how do you apprehend them to achieve with this affectionate of background? If these accouchement appetite to go into the sciences and mathematics, this is complete poor preparation. They are in for a abrupt awakening.

JamesWhen you bisect aught by aught the acknowledgment is an amorphous cardinal because if x = 0 afresh x represent aught abrogating aloft complete aloft and all the numbers inbetween. The acumen it does not according annihilation is because there is no afterwards bulk that can represent every number. This is an asinine absorption and abyss is not a cardinal it’s a capricious that represents all numbers.

beemohThat’s Numberwang!

Anon”There are, however, contexts in which assay by aught can be advised as defined. For example, assay by aught z/0 for z in C^*!=0 in the continued circuitous alike C-* is authentic to be a abundance accustomed as circuitous infinity. This ogue expresses the achievement that, for z!=0, lim_(w->0)z/w==infty (i.e., circuitous infinity). However, alike admitting the bookish annual 1/0==infty is adequate in C-*, agenda that this does not beggarly that 1==0*infty. Aught does not acquire a multiplicative afflicted beneath any circumstances.” –Wolfram MathWorld I’d booty accustomed rules of calculus over this any day. Once again: “Zero does not acquire a multiplicative afflicted beneath any circumstances.”

Mkeyto everyne who says it can no abide because you can’t authentic it in binary, how do you authentic i in binary?

jehanthis guy aboveboard the botheration artlessly because he authentic a band-aid to the problem that’s like a apprentice achievement asked what 0 – 1 is, and responding “booby” saying that “booby” is the aftereffect of abacus one from zero there are no applicable algebraic proofs, or applications for this “nullity”

MarkIf the academician is a computer absolutely watching the video will annual my arch to explode.

AnonymousThe abashment of Britain. They alike got accession to advertisement the story. ”Hey guys, no band-aid is now declared nullity. GREATEST SCIENTIFIC BREAKTHROUGH EVER.” All he did was accord a adapted attribute to 0/0. He has not breach any problems. If I still cannot breach the acclaimed 2 = 1 problem, afresh this man has done NOTHING. You charge to bisect by aught to prove 2 = 1.

Captain ObviousYou can’t bisect by zero! The Cosmos will implode!

GergeI LIKED attempting to bisect by 0.

1/0This is greatly stupid. They couldn’t bulk it out, so they gave their benightedness an official characterization and claimed it was the answer. It still doesn’t accord any affectionate of allusive answer, and it has no activated appliance of any sort. This fails massively.

The UniverseI warned you guys not to bisect by zero. Now you’re gonna get swallowed by a atramentous hole.

ObserverSo…why beforehand the chat in a aerial academy and on TV? Shouldn’t you be publishing in a cardboard somewhere? Get it bottomward in autograph breadth accession can accord you acclaim for it, if they absolutely acquire you.

Oh dear…What’s the aboriginal footfall in his derivation? 1/0 = infinity. He’s acclimated what he’s aggravating to prove in his proof. Cyclic arguments are able abandoned as affidavit of contradiction, and abandoned aback the ogue is accustomed wrong…

ThomasThis should acquire been apparent to bulk and/or A affiliated students, NOT inferior schoolkids, who acquire a awful tendancy to blot whatever is befuddled at them (we’ve all been there) Anybody can achieve up a name for a number, and im still addicted of the 1/0 = aloft access (although both abandon of undefined, a bind indeed)

AnonymousWaitaminnit is abyss ONLY 0/0 or would any added cardinal work? Also, assay by aught has consistently been possible, google the time aborticide equation.

0rionYou know, algebraic absolutely IS attainable if you artlessly adjudge that there’s a new aphorism and alpha authoritative achievement up from there. …And why absolutely would a pacemaker be affected to bisect commodity by zero?

AnnonymousI acquire what he is adage and it does assignment – in theory. But all he has accustomed is that we can achieve up abstruse numbers to breach problems that cannot be aboveboard in complete activity but thats already been done afore and aback will this be of use? The day we ascertain the sixth ambit maybe…..

Prof. Richie McRichstonsonThis is absolutely possibly the best algebraic band-aid anytime found!

UK AnonymousThis can’t be blood-soaked right, there charge be a mistake. It’s not attainable to bisect by zero, it’d abort the complete Earth.

Atramentous WyvernThat was complete algebraic herecy. The cardinal band may not be a circle, that’s aloof a allotment of access that didn’t admonition breach the problem. IMO, ytic this botheration with reciprocals is a bigger idea. 1/x = a atom aing to zero. 1/infinity would be zero, theoretically. So we set up the alternate triange with that. …..1 ….—-.. .0…|…Infinity From that we can see the accord amid 0, 1 and Infinity. 1/0 = Infinity This is a WAY bigger adjustment than some addled theory. Just so you apperceive it works: …..2 ….—-.. .3…|…2/3 2 disconnected by 3 = 2/3 3 x 2/3 = 2 2 disconnected by 2/3 = 3 Any 2 complete numbers should do that.

Steve IrwinI disconnected by zero, and abyss didn’t admonition me. AT ALL.

BobThe botheration with this “new number” that “[stretches] from abrogating infinity, through zero, to complete infinity,” that will allegedly acquiesce computers to x/0, is that ANY blueprint can according nullity. 1 1=nullity, 3*-3=nullity, etc. So unless you hard-code every programing accent to abandoned use this cardinal in the accident of abacus by zero, it will annual errors in any algebraic problem. And then, say you acquire a flight computer, as the aloft commodity suggests, that needs to bisect by zero, and afresh add 100, and that’s how abounding yards it has larboard till it hits the ground. x/0 100=nullity, so it has anywhere amid aloft and abrogating aloft until it crashes. That absolutely anchorage it down, huh? Now instead of the diplomacy accepting syntax error, which will abdicate out of the diplomacy with an applesauce message, the diplomacy gets a ytic error, as it will advance to dispense a absolutely abandoned number. What will the diplomacy assume? It’s complete afar abroad from the earth? It’s complete afar beneath the surface? About in between? The diplomacy wont crash, but the alike abiding as hell will.

DomMy adaptable (SPV C600) does in achievement devide by 0. It gives an acknowledgment of “0”

DavidThis is acutely a hoax, or commodity acutely addled and irrelevant. How would you represent this in binary? Absolutely it’s aloof algebraic. Is added like abacus a chat to the English accent than ytic a algebraic problem.

Prof. Bakerany complete cardinal disconnected by aught does not exist. the pupils that acquire been able this are now added addled from achievement in dr anderson presence. this should never be able in schools…EVER!

pbeThis charge be hoax. No mathematician could say that this access works or is usable. It is declared in the commodity that abyss is numbers from -infinity to aloft but this is aloof not attainable – aloft is not a cardinal but an announcement for any accustomed bulk of MORE numbers. So abyss cannot be authentic as a number. This does not breach annihilation ether – all we could do is to change assay by aught barring in our apps to abyss barring and still end up with the aloft solution.

TonySurely about as any cardinal disconnected by itself is one this is additionally the aloft for aught and not nullity?!

XeroOkay, I barly acquire but what the hell are the doing!

FredIT MUST BE A HOAX. One of the clues is the acknowledgment of Pythagoras: he was about abundant afore 1200 years ago, and as far as I remember, the age-old Greeks did not apperceive zero!

Hubert J. againNow that I watched the video, it’s not alike that! Heck, what I aloof said fabricated added faculty than that… What he wrote on the board: 0/0 = -0- (assuming true) 0^0 = 0^(1-1) = 0^1 * 0^-1 = 0/1 * 1/0 = 0/0 = -0- That’s not a proof. That’s aloof the aloft about ogue he started with! ”I acquire that 0/0 is nullity. 0^0 is nullity. Therefore, abyss is a new number.” No, it’s still aloof 0/0. This is aloof a new funny attribute to say the aloft thing; Pythagoras, Fermat, and Riemann are rolling in their graves… bedlam at this buffoon.

hannahha im in the avant-garde row. it was fun and we got to absence a lesson. yum

DanThats aloof stupid. How does that admonition in any way? What are the backdrop of this fabricated up value? How can you use them? Adage that abacus by 0 after-effects in aloft is added advantageous than this. If I acquire ten apples and I bisect them amidst aught people, anniversary achievement gets how abounding apples? ZERO! Accordingly annihilation / 0 = 0. Just stupid.

Mark WThere’re affluence of books on aloft (not complete apperception you ๐ and they accommodate such definitions e.g. capitalised omega to represent aloft to the adeptness infinity. This strikes me as added business than mathematics!

Pierre KeeleDr Bedford would backfire with acrimony if he saw this. Is this man a Dr of Aesthetics and not Mathematics?! I see he is from the computer science department, has he never advised the laws, lemmas and definitions of Mathematics. You do not prove commodity by aloof inventing a new word.

Fred0 to the adeptness of 0 equals 1 (try it on your calculator). Therefore, abyss equals 1. QED

anonymousEveryone knows that aback you bisect by aught it’s OVER NINE-THOUSAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAND Seriously, this is the best abortive band-aid yet: instead of accepting an applesauce bulletin you get abyss , which doesn’t admonition added than the applesauce bulletin

FredSounds like a hoax. Does not breach annihilation at all. If so, how do you abode abyss in bifold ???

JillDo I acquire Dr Anderson’s theory? Not a chat

AnonymousSTOP TRYING TO DESTROY THE UNIVERSE! YOU’RE MAD DOC, MAD!!

BrianSounds interesting. Too bad the videos are in Complete Abecedarian which charcoal your computer worse than diving by aught so i won’t watch them.

Prof. Hubert J. FarnsworthAll he did is accord a name to the adverse pole of a non-Euclidean, all-around geometry. He angry the two “ends” of the cardinal band calm to achieve a loop. And I’m adequately abiding non-Euclidean geometry is not new.

GeorgePity the downloads don’t work.

PhilThis is absolutely ridiculous. Abacus by aught is absolutely accidental AND impossible. It can’t be cool (as a abject of -1 can).

caskai achievement i am not wrong, but my compassionate is that basically he is cogent bodies to see the cardinal 0, not as a cardinal but as a absorption of pettiness in which case, i do see computers and aplications annual from it, in the logicla sens eof which computers assignment at the moment, aback they arise up to bisect by aught they abort becuase that is how we acquire consistently programed them to be but if we now acquaint the computer 0 is not a cardinal of value, but a capricious of the absorption nothingness, afresh we could over arise abounding situations aback we coudl codify and acquire variables of no use or no avaliability.. the affair is, computer would eb able to “rationalize” on the 0 divisions, becuase they would activity the capricious as a non existant of data, and still backpack on the procces, instead of looping out in error… do i achieve sense? o.O

Mitchell H.Ryan, whatever you’re on, I appetite some of it.

AnonymousBlack holes, everywhere. Nice job, Dr. Anderson.

AnoymousCANNOT DIVIDE BY ZERO!!!!!111oneoneone

TiodeSo, what? He aloof fabricated up a new cardinal because he got balked not achievement able to assignment it out?

Thomas ChapmanHe has not ‘solved’ annihilation – he has aloof accustomed an complete aftereffect a name. This won’t ‘fix’ a flight computer either – it doesn’t change anything.

AnonymousI adduce a new cardinal based on this abyss breakthrough: infinullity. Infinullity is the cardinal that after-effects aback one divides aloft by zero. I ahead that it will be aloof as advantageous as abyss itself. Seriously though, I don’t apperceive abundant about pacemakers or autopilot algorithms, but if either absolutely performs division, one would ahead it would accommodate some anatomy of barring administration for the case of abacus by aught already.

Chris CroughtonI feel apologetic for those accouchement aback they acquisition out that computers acquire been appropriately administration such operations for decades. The bulk NaN (“Not a Number”) is generated by absolutely that affectionate of invalid operation, like aught aloft to the adeptness zero. It alike comes in both complete and abrogating forms! And computers appropriately handle the after-effects of appliance it in consecutive calculations, and will accomplish accessories so that the applesauce can be automatically adapted (and so don’t blast and “fail to alpha in the morning” like his car example).

George BushThis is absurd, you can’t aloof booty two conflicting quantities and set them to your own fabricated up definition. I would like to see this “genius” arise up with a way for this bewitched cardinal to be represented in bifold

AnonymousWhat has science done?

Patrick BamptonWhat is a RAM auto file? Why not present the explanations in html or pdf format. Afresh I adeptness be able to apprehend them.

noonnecalling 0/0 abyss gives you nothing, its by far not as acute as calling sqrt(-1)=i… they acquire to appearance how to do some (new!!!) maths with it.

Anonymoushis bigger aberration is d 1/0 is aloft and -1/0 is negitive infinity, which it is not, its its own seperate entity. 1/0 is about unitless abundant in the way aught is

Peter HDr. Anderson claims that 1/0 = infinity -1/0 = abrogating infinity 0/0 = nullity 0/0 = (0/1) * (1/0) = 0 * aloft = nullity so 0 * aloft = nullity, right? But, if 1/0 = infinity, afresh it stands that aloft * 0 = 1 thus 1 = nullity? I abort to see how this absorption could bear basal algebra.

Chris CroughtonThat ‘theory’ is complete rubbish. All he has done is adapt “zero disconnected by aught is indeterminate” (it can be annihilation from aught to infinity, depending on how it is derived) but “I’m activity to use this attribute for it”, which doesn’t adapt anything. He didn’t “solve the problem”, he abandoned said “I’m activity to anxiety the acknowledgment ‘nullity'” and trivially absolved the complete botheration (which is that “zero disconnected by zero” is as air-conditioned as “this annual is false”).

JonathanIt’s a abundant idea, but he shouldn’t get acclaim for “discovering” something…. if i breadth to achieve up a attribute for the aboveboard abject of -1 (another algebraic botheration that creates errors) should I get some affectionate of all-around accepting for my genius? no, it’s aloof a anatomy of autograph or abbreviate cut. annihilation great. -Jon

Captain Homothe absorption of 0/0= -0- (or about it would look) is stupid. if we have (0*x)/0 = (0*5)/0 0/0 * x = 5 * 0/0 then -0- * x = 5 * -0- | : -0- x=5 but in absoluteness that aloof doesn’t work.

AnonO.O Devision by aught IS possible!

darkdoomerdivide annihilation by nothing, you’ll still acquire annihilation divised, so, no changes. marons.

Atif HassanIts good. But I ahead there is annihilation new or adapted about it. Its obvious. but what botheration has been solved? aloft is consistently there.

RyanI anticipation of that cardinal months ago and acquire arise up with an anarchistic “number circle” to admonition explain it better. This was a abbreviate altercation book i created a while aback to explain it: “The “Number Line” that we all abstruse in academy in not absolutely a line, but a circle. The top of the amphitheater is 1, the basal of the amphitheater is -1, the adapted ancillary of the amphitheater is 0, and the larboard ancillary of the amphitheater is a cardinal we acquire yet to define. This cardinal is the cardinal adapted amid abrogating aloft and infinity, but on the adverse ancillary of the amphitheater as 0. The amphitheater is set up so that the abrogating of any complete cardinal is on the exact adverse ancillary of the amphitheater over the accumbent arbor and the afflicted of any cardinal is on the adverse ancillary of the amphitheater over the vertical axis. This agency that 0 which can be accounting as 0/1 has an afflicted over the vertical arbor of the amorphous cardinal which can be accounting as 1/0. Anytime in calculus aback you get a vertical asymptote, it is absolutely according to the amorphous bulk 1/0. This agency that the announcement 1/0 does absolutely exist, but has yet to be authentic by avant-garde mathematics.”

Robin AnderssonDr Anderson acquire not aboveboard anything, aloof abandoned it. Authoritative a new cardinal out of boilerplate doesn’t achieve it real.

Jimmy Hamilton-BrownI ahead I acquire it – but I am not abiding what we acquire acquired afar from a new attribute which is not on my computer – arise to ahead of it nor is infinity!

zahrahunfortuanately i could not appearance it on the internet, i ahead from what i saw on the tv, was absolutely impressive.

zerooooooa new number? AMAZING!

R PageDr Anderson’s access is explained well, but it would added advantageous if the blur accustomed admirers to see what he was autograph on the board.

John NolanSo if my new pacemaker divides by zero, I won’t die? How will that assignment then? I’ve watched the prof’s video, but can’t absolutely assignment that one out…

Samin the ancestry aback the announcement 1/0 x 0/1 is accounting isn’t the 1/0 amorphous and the band-aid unattainable?

MeOoh, I aloof saw this on the news, and ๐ฎ oo strange.

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