Problems with Zero - Numberphile

[@UnexistingChannel]

Matt is very smart for a guy who writes infinity as double zeroes instead of a laying eight

[@marzi_kat]

What if he writes eight the same way?

[@rorschak47]

And X as two C having each other's back

[@OrangeC7]

@@marzi_kat It's treason, then.

[@TabooGroundhog]

@@rorschak47 Well that’s cause it’s a cursive x

[@lonestarr1490]

@JZ's Best Friend They would put him in a room with a quadratic floor and call it the Parker Square.

[@HECKproductions]

"glorified adding" is the best description of multiplying ever

[@BasicEndjo]

would that mean exponents are extra glorified adding?

[@shnob4916]

@@BasicEndjo glorified multiplication

[@BasicEndjo]

@@shnob4916 yeah and multiplication is glorified adding. then exponent is *extra* glorified adding

[@TnseWlms]

An article in the Onion from 1907 reported that a record breaking number of American children are staying in school beyond third grade. They are learning advanced skills such as multiplication, which we are told, is a powerful form of adding, resulting in numbers so large that three or even sometimes four figures are required to write them.

[@rishabhnitc]

This is what I told my 2 grader. “Fast addition”

[@p0ltergeists]

"BUT, if I am naughty..." Oh baby, talk nerdy to me~

[@karlcorrz]

LOL

[@yard2010]

+James Lynn Savage

[@f1f1s]

+James Lynn Rounding to the first decimal place also counts as naughty. Computing ∫e^x dx makes one horny.

[@stonecat676]

+James Lynn oh my lord

[@Closeuplogic]

pearl you're smart, what's the real answer here to 1/0

[@robotiquebleu9619]

My 7th grade algebra teacher would only whisper of dividing by zero because it would “upset the calculator gods”. He was one of my favorite teachers ever.

[@DaDonElChulo]

Great anecdote

[@malteepmeier]

My math teacher said he could taste numbers

[@ditian6234]

@@malteepmeier Ah, Synesthesia!

[@cones914]

@@malteepmeier mine snorted cocaine in class and offered some to us.

[@pxlbits6442]

@@cones914 Disgusting! Where is that teacher located? So I can avoid it

[@tiagojoseazevedoalvares1021]

"Only a nerd would tell you differently." *cuts to Parker* - Sooo, first of all [...]

[@dackid2831]

Even better "... and that's when you cut to Matt telling them differently."

[@Exploshi]

i clicked the [...] in ur comment wtf wrong with me lol

[@avi8aviate]

"And then we cut to a nerd telling you differently."

[@dontmd4158]

exploshi I clicked the [...] on yours😂

[@Kavafy]

thatsthejoke.jpg

[@aDifferentJT]

I suggest we define 1/0 = blue

[@blue9139]

Jonathan Tanner Look at me

[@CaseyShontz]

Jonathan Tanner make a petition

[@nataliaborys1554]

1÷0=blue. The newest axiom in mathematics.

[@bsm239]

x/0 = blue(x+1)

[@Xnoob545]

@@bsm239 1÷0=Blue×1+1=Blue×2=2Blue

[@snbeast9545]

For the "why does it return Error in a computer" question, the division assembly instructions (at least for x86) are designed to generate an interrupt when the divisor is zero. In other words, they are told to error out.

[@Xnoob545]

What would happen if they werent?

[@y-ax2-bx-c5]

@@Xnoob545 Presumably it would attempt that forever. It'd never find its result, and the part that tells it to stop has been chopped off, so it'll just never stop

[@Suicidekings_]

@@Xnoob545 setcomputeronfire.exe would initiate and well... You get the idea.

[@Xnoob545]

@@y-ax2-bx-c5 its like a minecraft world made out of sand Just falls fprever amd uses exponentaially more power

[@seushimarejikaze1337]

@@Xnoob545 cpu would hang at 100% usage trying to compute the result of what cant be computed, until you restarted it. therefore safety instruction/lock was added to prevent such.

[@andreaslam]

"The problem is it's a dangerous number and a lot of things can go horribly wrong with 0" "Mom I got 0 in maths" *UH OH*

[@savitharao7283]

Lol

[@tenplusten1116]

if it was art, it would’ve been better

[@mmmmmmmmmmmmmm5866]

@@boncoderz1430 you mean nice zero?

[@leyyes]

@@tenplusten1116 Especially if you're from Austria...

[@annxu8219]

@@leyyesuh oh…

[@ralfoide]

A video featuring both Matt and James is such a lovely treat. They are infinitely different.

[@anushkadas9267]

i see what you did there hahah

[@gddanielk8491]

Gosh you can’t say that

[@rhynosouris710]

An accountant, an engineer, and a mathematician are asked how much is 1 + 1: Mathematician: "1 + 1 is 2 and I can prove it" Engineer: "Well, 1 + 1 is anything between 1.8 & 2.1" Accountant: "It depends. How much do you want 1 + 1 to equal?"

[@JoeLinux2000]

Democrat: 1 x 0 = transgender Republican: 1 + 1 = homophobe

[@crackedemerald4930]

Quantum physicist: i don't know until i actually calculate it Surrealist: yes Communist: 1/2 for me, 1/2 for you, and 1 whole for the state

[@DeadJDona]

It depends whether we sell or buy.

[@jjjjj2220]

How to make a million dollours on paper with 50

[@naimy4511]

Numberphile: Imma head out

[@andrewjones5973]

Plot twist; the entire Numberphile series is a promotion for Sharpie.

[@KungFuPanda1223]

vihart???

[@NoahSpurrier]

Andrew Jones - And brown paper.

[@past12799]

I can smell the sharpies.

[@cadespaulding3837]

And the brown paper

[@EnerJetix]

DUN DUN DUN

[@flurng]

Now, I had always been taught that X/0 was "undefined", while 0/0 was "indeterminate". The logic behind this is that the denominator (or "divisor") should always be able to be made equal to the numerator, by multiplication with some factor. So, for example, 1/2 = .5, thus 2 can be made equal to 1 by multiplication with.5. However, in the case of X/0, there is no factor that can make 0 = X, since 0 times ANYthing is always 0. So, there is no correct answer, therefore, the problem is "undefned". On the other hand, in the case of 0/0, literally ANY factor will make 0 equal to itself, so there is no INcorrect answer. Thus, in essence, any value is equal to any OTHER value, which is impossible. Therefore, the problem is called "indeterminate", since one cannot determine what value best solves the problem.

[@Firefly256]

@Vikas Bhardwaj what if we define 0/0 as equal to 0

[@angelmendez-rivera351]

I know you said this is what you were taught, but it bears mentioning that this is just incorrect. There is no such a thing as "indeterminate" in mathematics, and people need to stop using this word forever. 0/0 does not exist. Period. That is all there is to it. And there is a very simple reason it does not, but it just has to do with what division itself is. Division is just multiplication: multiplication by the reciprocal, to be exact. 0 has no reciprocal. So one cannot divide by 0.

[@Firefly256]

@@angelmendez-rivera351 because in calculus, 0 is not exactly 0, 0 can be 0.0002 or -0.00001, numbers are not exactly their values. That’s why there is indeterminate

[@OptimusPhillip]

​@deaf I fail to see how those points connect. 0*x = 0 for all values of x is a true statement. I don't see how this implies that 0/0 = 1 any more than it does any arbitrary number.

[@OptimusPhillip]

​@@angelmendez-rivera351 Yes, in terms of numerical value, indeterminate forms are considered undefined. But they are very useful in calculus because of how they affect limits. (f(x+h) - f(x))/h = 0/0 when h=0, so it's undefined. But the limit as h approaches 0 is very much defined (when f(x) is continuous), and is in fact the definition of the derivative. If 0/0 is just undefined, derivatives don't exist, and calculus doesn't work. That's why we have indeterminate forms, at least when working with limits

[@MinecraftStonewideos]

*Santa:* You don't get presents this year because you were naughty *Mathematician:* What! Why? *Santa:* You used infinity as an answer

[@marilynman]

in high school I was doing a problem on the blackboard in an algebra class and I was finishing it fast so I was writing both sides of the equation (my way of doing it) and the teacher saw it and yelled "algebraic sacrilege!!!!" and that scared me lol and everyone else in the classroom. I swear that we almost hear thunders falling on us. Sufficient to say that I never had the opportunity to explain to him that I was still writing my answer, so I just completed the answer as a "correction".

[@circuit10]

@@marilynman You're supposed to write both sides?

[@marilynman]

@@circuit10 I meant that when you start writing it, you begin with the right side, you finish writing that side and then move on to the right side. I was doing both sides at the same time.

[@AKM-vo9lw]

X/0 = santa

[@caringheart34]

@Eero Naughty boy. Now you cannot wish to Santa anymore. Even finding out the meaning of life and solutions to infinity.

[@kcircuit8684]

1/0 = blue the secret is out

[@georgeabreu6392]

Lol.

[@ChrisBandyJazz]

Oh deah, it's a poblem

[@blackice7317]

He used a 1/0 Sharpie.

[@head_snapss7587]

Shhh, You're not supposed to tell anybody

[@gheorghegeorgescu3171]

Are you talking to Blue the Dog about the secret?

[@ChadDidNothingWrong]

1÷0= infinity 2÷0= Double infinity There I Fixed it

[@coulombicdistortion1814]

@Interesting Numbers Wait a minute, then you can multiply both sides by 0 and get 1=2. I think the Illuminati must be at work here. -lol

[@annoyinglyfast5972]

@@coulombicdistortion1814 Here's the thing about multiplying by zero: anything multiplied by zero is zero. So 0(1/0=2/0) (1*0)/(0*0)=(2*0)/(0*0) 0/0=0/0

[@neelamshroff]

Travis Ryno I have been stuck on this since last evening. My 13 yr old told me exactly this, and then used Banach-Tarski model to say that 1+1=1 is mathematically possible. I don’t know right now whether to believe his hypothesis or continue to say x/0 is undefined.

[@heathc148]

@@annoyinglyfast5972 He is saying that the logic is wrong

[@legomaster4213]

@Travis Ryno therefore 0/0=0

[@oreowithurea5018]

"Divide" -No "GlOriFieD SuBsTrAcTioN" - *YES*

[@debblez]

Substraction?

[@wobblyorbee279]

That is like roblox ad...

[@niccolopaganini1782]

Thank me for i was the 69th to like Jk

[@wobblyorbee279]

@@niccolopaganini1782 hello paganini

[@xuly3129]

0/0 = calculus

[@artschannel1359]

I love these numberphile videos because you can litterally notice how they get high on math as the video goes 😂

[@Halolaloo]

i see much enthusiasm :D I suggest "a hole in a hole in a hole" :D

[@emilyreynolds9206]

Math makes me horny

[@randomaccessfemale]

It's the only way to fly.

[@stargazer7644]

That's what happens when you inhale sharpies.

[@xexpaguette]

*Meth

[@downeykids]

Don’t expose them to sunlight, don’t let them eat after midnight, don’t get them wet, and never divide by zero

[@mistercherno]

I understood that reference!

[@jerry3790]

But it’s always after midnight...

[@rosuav]

Do not touch the operational end of The Device. Do not submerge The Device in liquid, even partially. Most importantly, under no circumstances should you divide The Device by zero.

[@steveheist6426]

AND NEVER EAT PEARS!

[@myownmeadow1320]

… And those are the rules for math gremlins.

[@marobottec1]

I divided 1/0 in my calculator and now it runs Super Mario 64.

[@farisakmal2722]

if I divide by 0 on my smartphone, can my smartphone calculate a rocket launch?

[@chaoticwaffle5487]

@@farisakmal2722 Probably

[@blue9139]

I divided zero on my table and now it can shoot lasers and fly

[@harleylequin3987]

ok............

[@namechangelol9815]

I inputted 1/0 into a sideways 8 and now every time I draw an 8, it Runs fortnite

[@gaymare6236]

12:49 "we could make it anything we want it to be depending on the angle we come at it from" sound life advice right there

[@ospreytalon8318]

3:05 Noooooooooo!!! Draw infinity as a continuous loop not two circles!!!

[@coconoisette]

It's ugly

[@disappointedcucumber]

@Al Gee Writing it as a continuous loop has a more comfortable flow than two separate circles

[@toniokettner4821]

two circles are not a lemniscate!

[@CubyChrisAnimations]

Yeah, the entire point of the symbol is being a literal neverending loop

[@reinhardtsanchez7952]

haha infinity go oo

[@sennahoj9332]

When i was a child. I thought 0 and -0 were different numbers, and i kept counting wrong when going from positive to negative or negative to positive

[@digitig]

In IEEE 754 format they *are* different numbers. They behave very much alike, though.

[@p.as.in.pterodactyl1024]

What's bigger, zero minus zero, or zero minus negative zero? Lol just kidding.

[@DrunkenUFOPilot]

@@p.as.in.pterodactyl1024 Who is bigger, Mr. Bigger or Mr. Bigger's baby? The baby, because he's a little bigger.

[@ΝίκοςΙστοσελίδα]

Original commenter: You were born with what is called "Ones' complement"! I guess you were upgraded to "Twos' complement" since then.

[@sennahoj9332]

@@ΝίκοςΙστοσελίδα What is that?

[@edgyspaghetti1122]

"And people will yell at me if i say its infinitely different" i lost it

[@thewhitefalcon8539]

There's a video around of an old mechanical calculator which gets stuck in a loop when trying to divide by zero, and the operator has to press the abort button to stop it running. Nothing bad happens - it just keeps subtracting zero and counting how many times it subtracts zero and it never finishes.

[@kead_davidson]

The way he smiles when he brings in the complex numbers...

[@looxluthor802]

And that all the while glossing over X^X for negative X looking really strange (it's jumping all over the complex plane and is basically discontinous everywhere). That is not a function for which you want to find a limit. The complex version must be just as bizarre.

[@liamdienemann8937]

7:44 "We're gonna slide it in and, in fact, we're gonna have to do it from both directions" O___0

[@thatoneguy9582]

Liam Dienemann “more than a numberphile”

[@Rudxain]

An Infinityphile XDXDXDXD

[@caringheart34]

There's a reason why infinity is drawn as two circles.

[@brunnomenxa]

Nice

[@themarsquatch420]

0 is my favorite number because it has no value, just like me.

[@jsbaasi]

I read this and I laughed. Thank you very much for that laugh. :)

[@spinn4ntier487]

ᎢᎻᎬᎠᎾᎠᎾ ᎬNᎢᎻᏌᏚᏆᎪᏚᎢ jokes on you, our numbers don't work without a concept of zero

[@fredericofp]

ᎢᎻᎬᎠᎾᎠᎾ ᎬNᎢᎻᏌᏚᏆᎪᏚᎢ CRAWLING IN MY CRAWL

[@lukelouis4034]

Bad day?

[@chhavigupta2802]

Ooh ..hope that was limited to being a joke.

[@puppergump4117]

6:10 Yes, computers are taught not to divide by 0. The reason is because bitwise math operations are only add and subtract. Multiplication is just repeated adding, while division is repeated subtracting. If you divide by 0, you are telling the computer to subtract 0 from the original until the value of the original is

[@keonscorner516]

≤ not

[@mdsharfuddinmd5710]

Happy New year sir

[@jathebest2835]

But Javascript gives back Infinity..

[@puppergump4117]

@@jathebest2835 That doesn't matter since the sign of the quotient is determined by the dividend. So are you going to get it as infinity or negative infinity? Since the answer is undefined anyways, is there a point in computing it?

[@puppergump4117]

@@mdsharfuddinmd5710 hi you too

[@gekfurian]

"Maybe this line goes all the way around and wraps around the entire universe and things come back up here" I'm having vertigo

[@digitig]

Not surprising if you know the history of the projective plane...

[@nanigopalsaha2408]

@@digitig *flashbacks

[@StevenAyre1]

I've always interpreted it as being positive and negative infinity and every possible number in-between. Not sure if that's valid though.

[@oerlikon20mm29]

@@StevenAyre1 yes, 1/0 is every number ever to be thought of at the same time...

[@mackycabangon8945]

"We can no more say that 1 divided by 0 is equal to blue" I lost it

[@meta04]

"we can no more say that *than* [that] one divided by zero is equal to blue" you missed a "than"

[@matrixarsmusicworkshop561]

@@meta04 ?

[@FishManChannel]

÷0 looks like a screaming person

[@IntergalacticPotato]

Yep

[@soulubilityofficial6635]

Fitting

[@100percentSNAFU]

It's screaming at you for trying to destroy the universe.

[@blue9139]

Thats the reason you cant devide by zero. But you can devide zero.

[@michelllozano6214]

Or like a key

[@EDoyl]

There's some great footage on KZbin of mechanical calculators, oldschool ones, dividing by zero. No programmed-in "Math Error" there, the things just spin forever making a racket, they're probably subtracting zero over and over but maybe some of them are failing in a more clever way.

[@SharpAssKnittingNeedles]

Error; task completed successfully 😂

[@MumboJ]

I consider 0/0 to be a feature, not a bug. Simple Algebraic Rearrangement tells us: If Anything * 0 = 0, Then 0 / 0 = Anything. Intuitively, 0 / 0 represents the question "what number can you multiply by 0 to get 0", to which the answer is clearly "Anything".

[@markkoehr5003]

If 0/0=1 and 0/0=2 then 1=2 by the transitive property. If you allow that, the you can say that every number is equal to each other.

[@MumboJ]

The transitive property doesn't always work that way. √1 = 1 and √1 = -1, but 1 ≠ -1

[@markkoehr5003]

MumboJ the square root symbol like that that is a function. when you use the square root symbol like that you are taking the principle root which is always positive. You mean to right x^2=1 which has to possible solutions that make that statement true. If you want the negative value you have to put the negative sign in front.

[@MumboJ]

Which is exactly how 0/0 works. It is a rearrangement of 0x=0, to which anything is a solution. Function Symbols are often used to represent this concept, and the phrasing I used was not incorrect.

[@awawpogi3036]

MumboJ a square root of a number can be either positive or negative. Its because both positive squared and negative squared are positive. Example: √1=±1 √4=±2 √2≈±1.414

[@Number_055]

Most CPU's have a specific return code for "Divide by Zero Error", meaning it doesn't attempt to calculate as the error is handled at the CPU level.

[@yvesisnotaname2813]

Number_055 return 0;

[@DanCojocaru2000]

I think it's implemented at OS level. And older operating system just tried to subtract 0 from the number forever, forcing you to turn off the power and turn it on again.

[@owlstead]

@@DanCojocaru2000 If you actually think that applications call the OS to perform calculations then you haven't got a clue what an operating system actually does and doesn't do. Division is not a system task, it can be performed by any application that is directly using the processor (CPU) at user level. Actually, most CPU's have division build right into them...sometimes incorrectly, check the Pentium bug (for floating point division).

[@majormalfunction0071]

Specifically, it's a hardware trap (ie. hardware exception) generated by the CPU at the time of division, at least on x86 / x86-64.

[@thatfield977]

Edit: I made a mistake in my original post, and I apologize. A divide-by-zero will return a "not a number" (NaN) result for a floating-point division. I don't know off the top of my head what result an integer division returns - this is something I should either look up or simply test - but the divide-by-zero register is still set, which can be queried to determine if an exception should be thrown. Floating point values may contain infinity and negative infinity as actual values, and if you want, you can treat a divide-by-zero as infinity, and I have in fact seen API's that do this, but generally speaking, you don't want a divide-by-zero to ever be a valid operation. Original post: @@majormalfunction0071 Intel CPU's will happily divide by zero and return either infinity or negative infinity, depending on the sign of the operation - they also differentiate between zero and negative zero; the sign is simply a bit in the return value. They will, however, as Number_055 noted, also set a "divide by zero" register notifying the application requesting the operation that a division by zero occurred, which the application may then treat any way it likes, including treating the operation as an exception and possibly crashing itself. I wholly agree that "infinity" is not a valid return value for a divide-by-zero, but the IEEE standards committee had to settle on something that would work from a technical standpoint.

[@poftim7773]

When you asked the old Sinclair calculator from the 70s to divide by zero, it actually tried! It would give you multiple answers one after the other until eventually it spat the dummy, showed all the decimal points and locked the screen.

[@benp9793]

spat the dummy? that isn't a phrase

[@toodsf1]

Ben P it is in Straya

[@psychotheunsane4542]

Multiplication and division are the next iteration of addition and subtraction. The iterations beyond those are exponents and roots. When you get beyond that, it gets really hairy. Layered exponents (also known as "towers") and roots (just the reciprocal of towers) are as far as most people dare to go. But you can technically go as far as you want, and Knuth invented a special notation to explain the weird realm beyond layered exponents/roots. It was used to create one of the largest numbers ever conceived, Graham's number.

[@JackFou]

For some reason, the way Matt writes his "x" is deeply unsettling to me.

[@taunokekkonen5733]

Shouldn't be allowed to work as a mathematician if you write x like he does LOL

[@clarkeysam]

How else would you do it? Like a normal written x?

[@taunokekkonen5733]

@@clarkeysam yes, you cross two lines like a respectable human being.

[@GeodesicBruh]

Tauno Kekkonen no, that x is anti calculus. You want a nice, curvy and sexy x.

[@skylardeslypere9909]

He writes it just like how you learn to write your x in cursive in second grade

[@blueberryboi9426]

Joke's on you, I divided by zero and got an answer. I put 1/0 in my calculator, and got "Error". So, 1/0=Error.

[@modvind]

Jude Pelaez makes sense lol

[@domantasbronusas]

basically, you get something, what programmer wrote. And of course he lies.

[@jospehas7850]

Jude Pelaez 0 divided by 0=error

[@U014B]

Jude Pelaez So 1/0 is the guy from Zelda 2? Brilliant!

[@Niom_Music]

Jude Pelaez but what about 0 divided with 'error'?

[@atherahmed6397]

I divided by zero and my calculator transformed into Optimus Prime and rolled out

[@bsm239]

my calculator prints out the entirety of Romeo & Julie and then splits into several people and performs it.

[@matrixarsmusicworkshop561]

@@bsm239 XD

[@iexplainjokestomakethemles1560]

So lame

[@eboone]

Greetings Mortal So lame

[@moosesurgeon]

A decade later and still a fantastic video!

[@oz_jones]

Ten, meaning one, zero. Coincidence? I think not!

[@DrummerRF]

The computer is actually taught to not divide by zero. There are many situations in software where dividing by zero is caught and protected against. My brother used to work in a hardware store and he had a computer that gave a 'divided by 0' blue screen. According to the story, he laughed insanely laud at that blue screen. Usually that doesn't happen but the computer had a defect RAM which fed corrupted data into the processor as it fetched the information to execute the micro programs. The processor actually had a build in protection to prevent dividing by zero, it stopped the operation and 'breached' away from its micro instruction to the error handling of windows which on its term showed the blue screen. In short, the computer doesn't even attempt to divide by zero. If you were to try and do it it would probably try to apply a form of implemented long devision which would obviously fail and I have no clue what it would return.

[@htmlguy88]

Robert sorry KZbin isn't letting me post my own comments one thing I would note for the people at number phile is it's as easy as defining 0*y=0 y in the complex plane but not =0 so 0 divided by 0 makes no sense since you can turn it into y*0/y1*0 the 0's can be seen to cancel and then you get y/y1 for any values y,y1 and therefore can take on any of any infinite values.

[@vitor.araujo25]

***** Actually, I think that algorithm doesn't quite simulate a division by zero because, for any value you insert as a divisor (if you swapped "int(n) - 0" for ,say, "int(n) - 3", for example), you'd still have an infinite loop (because the condition for the while loop will always be true and there is no condition for it to actually stop). A true general algorithm for a division of integers would be something like that: ----------------------------------------------------------------------------------------------- n = int(raw_input("Insert the dividend: ")) m = int(raw_input("Insert the divisor: ")) c = 0 result = n while True: result -= m if result < 0: remainder = result + m break c += 1 print c print "%d/%d = %d with a remainder of %d"%(n,m,c,remainder) -------------------------------------------------------------------------------------------------- If you insert 0 as the divisor, the "c" values will explode into infinity on the screen until you hit that close button, however, inserting other positive integer values would return normal division results. :D (also written in Python, because screw it, i'm on that lazy train too \o/)

[@szlomajosif2711]

Robert Dividng is reverse of multiplyin so: 4/3 is 4 * (1/3) and a proof of this is that: (4/3) * 3 = 4 (a/b) * b = a so: if b = 0 and a is any N then a =/= a which as answer is not in set N because any a in this set is equal to itself (4/0) * 0 = 0 ==> 4=0 The result of this nonsene came from the set. Any result on the corpus of N must result in the corpus of N and 0 is not in even in the set of N.

[@robertfennis6088]

Szloma Josif Point being?

[@szlomajosif2711]

Robert Fennis Set dosent include result. Need a larger set with algebra over biger corpus with a diferent ring and more dimensions. And of course problem is solved, directX is working perfectly without gimbal lock on this wee issue of dividing by zero.

[@SarahC2]

"We have to slide it in, from both directions." - Phwoar........

[@anonymousaubergine4455]

stop. lets keep it PG

[@rlrsk8r1]

+Sarah Cartwright Hi Sarah!

[@MagisterMalleus]

+John Yyc zero ain't PG mate. Zero is a dirty boy.

[@matrixphijr]

+Sarah Cartwright "So you say, 'Well, if it doesn't matter which side we're coming in from... surely we can just call it one.'"

[@matrixphijr]

+John Yyc Even PG movies are allowed brief adult moments.

[@АлександрАфонин-я8щ]

From the software engineering perspective I'd say that I highly doubt that any commonly used calculator uses iterative process to get an answer for X/0. It's just a check in the code: if operation is division and second argument is 0 then print "Error". So, the first guess is much closer to reality

[@leechbeen3283]

Definitely more likely. Calculators only really do addition and subtraction so if you tried to divide by zero it would keep subtracting by zero an infinite amount of times, just like they demonstrated in the video. Its gotta be programmed to check for a non zero number to keep it from entering an infinite loop, that seems like the best solution

[@Stettafire]

This is how most applications work, most of the time its baked into the compiler (Roslyn)

[@patrickvolk7031]

It's normally an exception, stopping your execution. If you have a divide by zero in your equation and you don't stop, you're in la-la land. CPUs handle integer division (which give division by zero and overflow), languages have standard libraries for floating point. The standard is to have zero, NaN (Not a number), Inf, and -Inf as distinct results. Most calculators now have this as well (processors are very cheap). NaN is different than infinity. Infinity normally means it encountered a number which exceeded the maximum value (e.g. 300 factorial), and infinity times zero is zero. Any math operation using NaN gives you NaN as a result. You also can have exceptions for overflow/infinity, and there may be cases where you want to know when you underflow (if you have x and y, which are not zero, but you get zero because the number is too small.. that's not normally one you worry about). A difficult problem in programming is when you have a one-off problem, where it goes into la-la land, and takes a few steps before it dies. Math is one of those things.

[@hareecionelson5875]

Unless someone forgets to tell the computer not to attempt the subtraction, in which case the computer may crash, which happened to an American warship, computers down for a day

[@mdsharfuddinmd5710]

Happy New year sir

[@sulfurx777]

Also, it can’t be infinity, because even if you subtract it an infinite amount of times your still going to have the number you started with.

[@Vespyr_]

But all division does is count the subtractions that took place to reach the number. Therefore, it isn't infinity or the number you started with. It's 0. 20 / 4 = 5 (Five Subtractions) 20 - 0 = 20. No subtraction took place. 20 / 0 = 0 (Zero Subtractions)

[@angelmendez-rivera351]

@@Vespyr_ No, that is horribly incorrect. Firstly, that is not how division actually works: division is not repated subtraction, and multiplication is not repeated addition. Secondly, even if division did work that way, your answer is still wrong, becaue 20/0 would be equal, by your definition, to the number of times you have to subtract 0 from 20 to achieve 0. The problem is that, even if you subtract 0 an infinite amount of times from 20, you still do not achieve 0. The answer is not 0, nor is it an infinite number. It is just impossible to achieve 0 via such repeated subtractions, hence 20/0 is undefined. Nevermind this, because as I explained firstly, division is not repeated subtraction. The reason division by 0 is problematic is because, in order for division by a quantity A to be possible, you need to have the following property: if A·x = A·y, then x = y. This does not occur with 0. 0·1 = 0·(1 + 1), but 1 = 1 + 1 is false, in general. So division by 0 is hopeless.

[@aaykat6078]

The answer is super existence, a level above every number

[@thefloormat3297]

@@angelmendez-rivera351 I think you missed the point of glorified subtraction but that idea does work, 28 divided by 4 is just 28 minus 4 over and over till its 0, which is when it's been subracted 7 times

[@angelmendez-rivera351]

@@thefloormat3297 No, dude, I literally addressed it within my first sentence. Maybe you do not know how to read. Also, I already explained how subtraction does not work. You cannot subtract 0 over and over from 20 until you get 0. It is impossible.

[@asmod9537]

I met this channel a while ago, when i was in highschool and used to watch every video. Now, as i'm graduating in mathematics i come back and rewatch the same videos, but now in a different perspective. Numberphile was one of the main reasons i decided to study math in college, despite all flaws.

[@squee222]

Mathematician: "you can't divide by zero" Engineer: "Just watch me!!!"

[@JoeLinux2000]

That must be what Denny Pate, the designer of the FIU bridge did, and then the Boeing engineers that designed the 737MAX followed his lead.

[@Rashidamin]

Oh c'mon, it's usually the otherway round. Unlike mathematicians, engineers are too boarged down with deadlines and budget constraints that they hardly have any luxury to play with theories and concept. Otherwise the boss would show them the door 😅

[@woofwoof7168]

2:20 - 2:30 But 1/0 is equal to blue.

[@rishan2235]

2:25Mathematicians definition if “naughty” and “evil” - “Ooh, what if I said 1/0 = infinity? Ooooooh”

[@lucabonisoli]

Here's a simpler explanation of why n/0 is impossible and 0/0 is undefined. I use it in my 6th grade classes in Italy using numbers instead of letters. 1) division is the inverse operation of multiplication. Calculating a/b means finding a number (let's call it "c") that multiplied by b gives a (in other words, c*b=a is basically the same thing as a/b=c, you're just reading it backwards. For example: 6/3=2 and 2*3=6 are basically the same thing, you're just reading it backwards). 2) if b=0, then you get a/0, which is impossible because there's no number that multiplied by 0 gives a. In fact, a/0=c means c*0=a, and there's no number "c" that multiplied by 0 gives a. Since the operation a/0 doesn't have a result, it's impossible. 3) if a=0 and b=0, then you get 0/0, which is undefined because any number multiplied by 0 always gives 0. In fact 0/0=c means c*0=0, which is always true, no matter what number "c" you choose. Since the operation 0/0 doesn't have one single result (it has infinite results), it is undefined. I hope this can be helpful.

[@sixthSigmaSnowball]

6:14 the answer for the calculator is defined by IEEE floating point standards and generally requires that software implement exception handling such that when the processors encounters a divide instruction with a zero operand it generates the divided-by-zero exception so the software can decide what to do.

[@reapinit8777]

Drawing X as two half circles? Classic Parker Square.

[@Bignic2008]

Lots of people do this. You pick up handwriting habits like this so you can more easily distinguish between symbols that look the same. x and the symbol for cross products, for example, look similar and will confuse people unless you draw the letter x as half circles.

[@smockboy]

This is a relatively common convention tbh. It was specifically adopted so that 'x' would be more readily distinguishable from the multiplication symbol in mathematical proofs and textbooks. A common alternative was to use * as the multiplication symbol, as most scientific calculators do.

[@ineednochannelyoutube5384]

That looks more like a khi

[@reapinit8777]

@@Bignic2008 thats actually pretty cool. Definetivly reasonable. 👍

[@reapinit8777]

@@smockboy makes sense and is smart 👍

[@NighT-WolF85]

11:23 Even the painting is interested in mathematics.

[@lombridious]

lOL

[@SebvdBergh]

I think James' first description is pretty much perfect. You just keep subtracting a number until you get to zero. If you did 20 - 0 an infinite number of times, you'd still end up with 20, because every step leaves you with 20. So infinity essentially has no effect on subtracting (or dividing by) zero.

[@JackLe1127]

If I had numberphile as my math professor, Vsauce as science, I would top the school.

[@Super.AmmarI0]

I don't think Vsauce knows curriculum science. He is only interested in the abstract and ambiguous topics of science.

[@kur1tan]

That is the craziest way to write "x"

[@SirNobleIZH]

I recently learned what the actual name for 0/0 is in Calculus. It's called an indeterminant, because it can give any answer. If we want to solve it, we need to know the function that created the 0/0, as they show. Then we take the derivative of the top and the bottom (separately), and try to divide again. We repeat until we don't get a 0/0

[@maddoxmayo]

L'Hopital's!

[@cpotisch]

That’s not quite accurate. An indeterminate form like 0/0 is entirely meaningless on its own and fundamentally can not be “solved” unless you’re talking about in terms of a limit. Furthermore, 0/0 isn’t the only such form, so your use of L’hopital often isn’t applicable.

[@gamerdio2503]

@@cpotisch All the other indeterminate forms can be turned into a 0/0 or inf/inf form, in which L'H can then be applicable

[@cpotisch]

@@gamerdio2503 e^x-x as x goes to infinity?

[@gamerdio2503]

@@cpotisch Fair enough. Most of the time, the indeterminate form can be converted into a form usable with L'H. Although, you can just use the fact that e^x grows faster than x to get a quick answer

[@Lord_Skeptic]

I divided by 0 and my paper set on fire

[@oerlikon20mm29]

Yea, I tried it on my Samsung 8 and it exploded

[@memebeans1589]

BEANS

[@Lord_Skeptic]

No that is what 2 beans add 2 beans is

[@Lord_Skeptic]

That is actually some beans

[@Lord_Skeptic]

Or a really small casserole

[@suddenrushsarge]

OH GOD NO... He's gonna divide by zer....................

[@Duviann]

+Sarge!!! BOOOM

[@maximo1590]

Dewey russian kh/ch -Хх

[@pepe6666]

hey i heard someone divided by zero. is everyone okay?

[@noahdavid5258]

(Bomb explodes)

[@m_affiliates]

⚫️

[@davidlones365]

1 / 0 = infinity 2 / 0 = infinity 1 = 2 Nonsense, right? 1 * 0 = 0 2 * 0 = 0 1 = 2 Yep. Nonsense.

[@NoRotation]

To get 1/0 = 2/0 into 1 = 2, you multiply by 0 on both sides, which we currently say is well defined. To get 1/0 = 2/0 into 1 = 2, you divide by 0 on both sides, which we see we cannot define unless we throw out multiplication by 0. A lot of things seem like nonsense if you don't pay attention in class.

[@t7H2si0vß2]

***** I agree, ( lim x→|∞| ∀x[∞] →∃x[x/0=|∞|] )

[@computerman4321]

And this is simply because infinity and 0 are both concepts, not numbers. It is present in mathematics because it is quite useful, such as algebra but to an extent. The very first number systems didn't include a zero at all, some argue that this is why the Roman Empire has fallen.

[@t7H2si0vß2]

PureAwsomeness thank you, i agree entirely.

[@abcdefzhij]

I hate when people say that. All numbers are "ideas", and zero and infinity are numbers the same way 3 is a number.

[@juliusking5126]

I still remember that day when I was in the middle school. Our math teacher, let us use 1 divide some positive numbers smaller and smaller, than we found the results bigger and bigger. Then we use negative numbers bigger and bigger, and the results were smaller and smaller. On that day all of us remembered we cannot use some numbers simply to divide 0.

[@DrDerp42]

If 1/0 equals infinity, the that means infinity times 0 equals 1, which is not possible.

[@thanos486]

0χ(+-infinity) is an undefined number so it can be 1 as well

[@yoavco246]

You can't just treat infinity as any other number. It is an idea, not a value you can do operations on.

[@thanos486]

I did not say that infinity is any number.I said 0x(infinity) is an undefined number so you dont know whether it is equal to 1 or not , therefore you can not say that 0x(infinity)=1 is an impossible equation, it is an undefined equation. And you can do operations on infinity. For example: (1/infinity)=0 and: (+infinity)(-infinity)=-infinity

[@yoavco246]

+Tomas Cena I was refering to the main comment :)

[@folf]

DrDerp42 This is a dangerous subject

[@Aaron4309]

0/0=0 and 1/0= 10^infinite 0. If you want me to explain i am more than happy to. Another theory is that anything divided by 0 actually equals itself. ( 1/0=1 )

[@sophieward7225]

So a lot of these arguments are akin to the arguments used against imaginary numbers, basically saying "it doesn't make sense." But, like imaginary numbers, why can't we just say, "okay, sure, they don't make sense," and declare that they exist, just to see where it takes us? We did it with numbers larger than infinity (see that long and mindnumbing VSauce video), so why not with "supernihlic" numbers?

[@underrated1524]

If I understand my computer science right, computers' physical arithmetic processing units throw errors when they're ordered to divide by zero, which would cause horrible breakage. In practice, though, the command to divide by zero is intercepted by stuff like the operating system long before it actually manages to reach the hardware.

[@Bayar-oe7rj]

Infinity is not a numbah... It can't be treated like a numbah... I love that guy 😂😂😂

[@MrPianoKnee]

Infinity is certainly not here but it is certainly over yonder.

[@areadenial2343]

In many cases, zero can't be treated like a number either. So should we just say it's not a number and call it a day?

[@Ph0n3numb3r]

@@areadenial2343 but zero is defined, its when there is nothing. But infinity is undefined, because no value can represent it. "Oh, the biggest number is 10^99999", "well, what if i add +1?".

[@areadenial2343]

@@Ph0n3numb3r You're half right... no *finite* value can represent it. Because you can't represent an infinite value with something finite, who would have thought? Really, infinity is the opposite of zero. Zero represents nothingness, a lack of value. Infinity represents eternity, a never ending value. So, a 1 followed by a never ending trail of zeroes. It just keeps going, forever.

[@mariafe7050]

*number

[@BaggyTheBloke]

11:50 I see what you did there, NAUGHTy

[@poggy9635]

Freaky Fred :)))))

[@thomasraahauge5231]

Who said that mathematicians can't be naughty?

[@andrewdotsonexplains6948]

6:25 totally agree with that. I know that when I do a really intense calculation on Desmos, the calculator displays to me a message saying "definitions are nested too deeply"

[@kaif_.]

The way he writes Infinite Haunts me 3:07

[@raoulhery]

But if you push too hard...even numbers got LIMITS

[@LongNguyen-pv9sm]

that because they set a limit in the first place, they set it to zero, if i don't set any limit, it would go forever

[@anoukkadijk1656]

Salvador Allende those limits are "errors" (paradoxes) in the system we made

[@ryadachaibou8098]

He's quoting a Mos Def song called Mathematics.

[@brendanotoole5871]

If you don't know, now you know...

[@andrewmirror4611]

What about odd numbers, they got limits too?

[@oscarelenius4801]

He draws graphs with arrows on both sides of the same axis. Would rather divide by 0

[@evajanin2970]

Why is this so far down!!! Goddamnit that irritates me

[@Dragongaga]

Yeah. Because the graph of rational numbers goes in both directions

[@Ivan-yy4ng]

@@Dragongaga yeah and that's correct i guess

[@sohee7597]

I don't understand, I draw my graphs like that

[@luxon4]

yes thats by definition correct where on earth did you. go to school that they didnt teach you that, have you never drawn a graph before?

[@No-pm4ss]

Can you talk about rooting negative numbers?

[@jdude99lolz]

victor sodéus i think they have videos on complex numbers. if not there is a really great 13 part series by another youtuber.

[@lrgaetz5679]

"\" will be square root. 2\-1 doesnt work (2 numbers the same, multiplied together are always positive: -1*-1=1 but 3\-1=-1. if the "n" is odd it will be -1. if its even, it equals nothing (exept perhaps 0^0)

[@randywebb8284]

Bacon Grease, i^2= -1 by definition. Creates the Complex Numbers and you can have a square root of a negative number.

[@lrgaetz5679]

no real number squared will be negative. ever. if you square any number, by deffinition it becomes positive. i said real numbers.

[@jdude99lolz]

Bacon Grease nowhere in your comment did you say real numbers though.

[@philipsmith1990]

A long time ago Mr. Talbot, my maths teacher, said that we can't accept dividing by zero because if we do we can 'prove' false things. I can't remember exactly how he did it but he proved that 1 = 0. He then said that if you can 'prove' one false thing you can 'prove' any thing that is in fact false. A quick google found this; x and y are 2 non-zero numbers where x=y. So x^2 = xy. Subtract y^2 from both sides, X^2 - y^2 = xy - y^2. Divide both sides by x-y we get x + y = y which is clearly false. Dividing by x-y when x=y is dividing by zero. which is why this goes wrong.

[@FlyNavy906]

Dividing by zero is such a Parker Square move.

[@M00nSlippers]

lol, only numberphile fans will get this.

[@DoomedLich]

Usually the way I explain it to people is that almost the entirety of calculus is an attempt to simulate dividing by zero. There's that entire branch of mathematics (which most people find too complicated to be worth learning) that is pretty much just answering this question, and it's still a fuzzy and imperfect answer. So if you wanna see why you can't divide by zero, a basic overview of calculus often will do the job if it's being explained well.

[@matrixarsmusicworkshop561]

But u can

[@eljakimdeclerck1941]

see me divide this cake into zero pieces!! NOM NOM NOM

[@BadWebDiver]

The cake is a lie!

[@vibodhj349]

You aren't dividing the cake, you are 'subtracting' it.

[@bigbee9878]

I agree with you. See my comment.

[@grandexandi]

I know it was a joke, and it's funny, but I feel impelled to point out that you simply divided 1 by the number of bites you took, and if there were no leftovers, then zero is the remainder, not the number you divided by.

[@ianbuilds7712]

20-0=20, 20÷0=20 and cake÷0=cake just like cake-0=cake

[@jsolivas1516]

I always hated math and no one I know likes it, but it is nice to see people with a real passion and love for maths/numbers to make it more interesting

[@MrCmon113]

This video: "You can't say something is equal to infinity!" Other video: "1-1+1-1+... is totally 1/2, no problem here, guys!"

[@ivyssauro123]

The way you write the 'X' and the 'Infinity symbol' is so weird!

[@typo691]

"You"? Which "you"? There's 2 people we see in the video, which one are you talking about? ...Or do you mean the plural "you" and combined both of them?

[@ivyssauro123]

Typo No idea, the one who does it wrong.

[@ivyssauro123]

Jay Jeckel Come to think of it I think he does it on purpose. Because in the end it serves the same purpose and it's just a formality, he probably does it for fun to get under his mathematician friends skin.

[@jayjeckel]

Ivo Wilson I always assumed it was because he is from the UK and they do some things weird over there, like calling math 'maths' and sports 'sport'. Could be easier drawing on a chalk board or what you said. Either way, he does some great videos and his channel is worth checking out if you haven't already.

[@ivyssauro123]

Jay Jeckel Absolutely, I did check it out and even though I'm not a maths guy I fell in love with it

[@zerocalvin]

1/0=Blue... i'm going to write that next time i write a calculator program..

[@monkeseeaction21987]

"anything divided by zero is counting to infinity." Vsauce: *how to count pass infinity*

[@gandolph999]

Division by non-existence? It makes no sense.

[@salty_slug]

Also, dividing by zero doesn't work because 1 would then equal 2 lets say this: a = b a^2 = ab a^2 - b^2 = ab - b^2 (a-b)(a+b) = (a - b)(b) and here, you would say that you could divide by (a - b), and if we do a + b = b b + b = b 2b = b 2 = 1 the problem is dividing by (a-b) which in this case is zero

[@thierrykortekaas6356]

These numberphilr videos with multiple interviewees are among the best!!!

[@HayTatsuko]

anything divided by zero = 42 come on people! don't you know your DNA?

[@SpectatorAlius]

You must be descended from the telephone sanitizer;)

[@ATBPjako]

so zero = life?

[@thatonetacobellguy]

ATBPjako Since 0 can be defined as Nothing or None, 0 = 42 could mean "You have no life"

[@julekmeister]

If anything divided by 0 = 42 and 42 is the answer to the ultimate question, then anything divided by 0 (x\0) IS the ultimate question. That means that the answer to x\0 is the meaning of life and everything else. Come to think of it, lim x->0 = infinity (positive or negative) but never reaches 0 itself - it's composed of everything in the universe except for a point where there is nothing. Oh man, I don't know, if you catch my drift. I'll call it Caldoon-Adams-Julekmeister's Law of Relative Existence :)

[@santerirautamaa9479]

Even the number of likes on your post has been divided by zero

[@somedudeok1451]

This is my favorite video on this channel. Makes me chuckle every time.

[@brankodimitrijevic382]

3:16 infinity is actualy a duble zero :D Was that on purpos???

[@andrewpersaud4144]

The rebels are coming, with their "Free division by zero" picket signs.

[@tonyrosam]

Negative infinity plus positive infinity is zero. The graph made perfect sense. They are symmetric mirrors of each other and cancel out. both exist at once to make the curves cancel.

[@DrDeFrE]

If negative infinity plus positive infinity would always equal zero, the following would hold: (+inf) + (-inf) = 0 lim(x) + lim(-2x) = 0 lim(x-2x) = 0 -inf = 0 You get different results depending on what you put in. That's why you say it is undefined.

[@tonyrosam]

you look at both solutions interacting with each other on graph.

[@TheMrKeksLp]

You cannot do arithmetic on infinity, it's not a value

[@PC_Simo]

The way I see dividing by 0 being nonsensical, is thinking of division as reversed multiplication (which it is): 20/4 assumes there is a number that, when multiplied by 4, equals 20; and there is. It's: 5. Dividing a (non-zero) number by 0 assumes there is a number that, when multiplied by 0, equals that (non-zero) number; which, obviously, isn't true. As for 0^0, it's just (0^1)/0 (since a^0 = (a^1)/a) = 0/0, which could literally be anything, equally likely. The reason, why people say: "a^0 = 1", is, because a^0 = (a^1)/a = a/a, which *_USUALLY_* equals 1; but that reasoning doesn't really work with 0, as discussed earlier.

[@TarexEsserTaavao]

Have you guys done anything on 1/infinity? Or is that even allowed (since "infinity should be considered as an idea not a number)?

[@charliespurr7325]

Lol the calculator on my phone says 0^0 is, quote, "Undefined, or 1."

[@MuffinsAPlenty]

Same for my phone, and honestly, it's the best answer I've ever seen a calculator give, considering what mathematicians say about 0^0.

[@blauesserpiroyal2887]

Mine says both 0/0 = ∞ and 0^0 = 1. I think this isnt the best phone calculator.

[@thesparksplug]

Because zero has no value, working only with zeros makes no sense. 0^0 is the same as saying 0/0 which is, in actuality, I have nothing and I don’t divide it what’s the answer. See? That’s totally nonsensical. Lol

[@xexpaguette]

I got *Error* on a MacBook and 0 on my android phone

[@xexpaguette]

@Milan Duchevski 1/0 is 1.

[@TacoStanMan]

If you look at zero in terms of inversion, zero is essentially "neutral infinity", in a way. If you take the inversion of zero with any base radius, you will get a variation of infinity as the answer.

[@swbrl2843]

I think you're confused in that you are making weird calculations based on our imperfect, artificially created interpretation of mathematics. Doing a bunch of maneuvers isn't proof that nothing is equal to everything, it's just a flaw in the math we created.

[@zxuiji]

Here's another way of presenting N / 0 = 0 (written in Lua syntax): N = -1 C = 0 while C > N do N = C R = A - B C = C + (A > R and A >= B) A = A - B end

[@Hypastpist]

im surprised they didn't explode

[@EpicB]

0^0=Spaghetti

[@paein9642]

Hm I thought it was banana

[@protoxus8186]

+Bearboy03 No, 0^Spaghetti is Banana. You were close, though. :)

[@shekharmaela2308]

+Naveek Darkroom 0^0 = 0

[@shehabkhan637]

+Marcus Johnson Lol - Unless you are having fun, 0 ^ 0 is not 0 :P it's.............................1

[@shehabkhan637]

+Marcus Johnson - You sound like a guy back in the 17th Century, "0 is nothing"??????????? Just...wow... I laughed quite a lot when i read that... You made my day XD

[@Reydriel]

I have a few thoughts, though I may be wrong about a few things here. Why is it that when you approach 0 from the negative side of the function 1/x, it goes to negative infinity? Doesn't that imply that 0 is a positive number, since a negative number multiplied/divided by a positive number equals a negative number? Even if we have -0, it would just be "corrected" to just 0. What gives? :P

[@nychold]

(1) Because as you approach 0 from the left, x will always be less than 0 (definition of negative). Since 1 is positive, a positive divided by negative is a negative. Since you're taking a limit, you never actually get to 0, but the closer you get, the more negative the number becomes, so you say it approaches negative infinity. (2) No, because by the definition of limits, you don't actually reach the point you're approaching. Limits are used when there are singularities in math (values for which something undefined or impossible happens). You're absolutely not allowed to plug that number into your expression and get a value, so you take a limit...you get really close and see if it's approaching a value. (3) Zero is neither positive nor negative, so the rules of positives and negatives don't apply. In fact, by definition, it couldn't be positive or negative even if you wanted because it's part of the definition of *both* positive (greater than 0) *and* negative (less than 0). The reason that +0 = 0 = -0 is because of how you can turn a unary operator into a binary operator. For example, -0 (unary because there's only one term) is the same operation as 0 - 0 (binary, two terms), which of course is 0. +0 is the same operation as 0 + 0, which is still 0. Neither unary operator (when converted into an equivalent binary operator) had any affect, so 0 must be special in that respect.

[@TheBawbSaget]

0 is not negative nor positive, it is a point. Saying '-0 and +0' is like saying '-axis and +axis.' The reason X (of 1/X) approaches -∞ from the left is because it is being divided by infinitely smaller negative numbers, not 0. The definitions of positive and negative are literally 'greater than and less than 0' respectively; there is no definition for '0 = 0' other than, well, 0.

[@markdanielcastro]

when you say it approaches to 0 from the negative side. It means that x is not 0 but very close to 0 so in this case x= -0.00000......1 so you can't correct the negative sign.

[@acomputer121]

But it never does reach negative infinity. You CANNOT divide by zero. As you get closer to zero from the positive direction, it goes positive infinity, and you get closer from the negative direction, it goes negative infinity, but at 0, there is no value (and no it doesn't cancel out to 0 either! That'd be equally as troublesome as it equalling infinity).

[@RhetoricXZ]

0 Is actually considered a positive number.

[@AbhiMule404]

Software developer here: We don't try to solve it by any method... we throw error for situations like this 😂

[@AbhiMule404]

@@ForeverStill_Fan1 start with C or C++ Understand the basics of programming... Don't directly jump to python... Python is a high level language doesn't help too much for building logic... For frameworks- depends on your interest

[@jtmitchell82]

Is this 'partially' why physics seems to only discuss the big-bang meaningfully at times or intervals after it has began?

[@Acc3ssViolation]

a^0 = 1 and 0^a = 0 can't both be true if a = 0, because then 1 = 0. So for that reason alone 0^0 can't be defined.

[@Inspirator_AG112]

_This Comment is cross-posted!_ *0^x = 0* is _only_ true for _positive_ exponents!

[@Inspirator_AG112]

_This Comment is cross-posted!_ 1 is a more consistent answer. The *Taylor expansion* for e⁰ will be *0⁰/0! + 0¹/1! + 0²/2! + 0³/3! + ... = e⁰ = 1.* The only term that is not 0 is *0⁰/0!.* There is also the *Taylor expansion* for *cosine.* If *n* objects each have *k* states, then the equation for the number of the set's positions is *n^k.* Think about the number of positions that [a set of 0 objects each with 0 states] has. This is philosophical, but it is one state. As for *0^x = 0,* that is only true for _positive_ exponents of 0. The Binomial Theorem also relies on the *0⁰ = 1* statement. As for limits, those are only accurate to the true value for continuous functions. Take the piecewise equation *y = x if x ≠ 5, y = 1 if x = 5.* The limit of y as x approaches 5 is 5, but *y = 1* AT *x = 5.* As for the *Product&Quotient Rules* of exponents, under certain circumstances, those are false for 0. I hope this makes sense.

[@FanTazTiCxD]

5:50 The look you get, when you're on a date with a mathematician

[@Mr_Peachyy]

he’s rizzing us up 💀

[@NerdWithLaptop]

Matt: you can’t divide by 0 Little kid: *gasps* James: *draws two circles to mean infinity* Me: *gasps*