Why is 0/0 undefined?

Think of it like this.

10/5=x
>"how many multiples of 5 does it take to make a 10?"

0/0
"how many multiples of 0s does it take to make a 0?"

It could be 1. It could also be 2. Or 1 million. Anything and everything is the answer to this one, really, so it's not defined.

1/0
"how many multiples of zero does it take to make a 1?"

This one is undefined for an entirely different reason. No matter how many zeros you add up, you'll never approach 1. Even if you have an infinite number of zeros their sum never surpasses zero. The answer is undefined because it's an impossible request.

Actually if you add infinite zeroes you get 1

Proof
0.999... = 1
1-0.999... = 0
0.999... + 0.999... = 0
0.999... = 9/10 + 9/100 + 9/1000 ...
1 - 9/10 - 9/100 - 9/1000... = 0
(1 - 9/10 - 9/100 - 9/1000...) + (1 - 9/10 - 9/100 - 9/1000) + (1 - 9/10 - 9/100 - 9/1000) ... = 1
0 + 0 + 0... = 1

shit tier /sci post as usual

>0.999...+0.999... = 0
actually it would be 1.999... not 0. go back to /b or /x, where ever you crawled out of.

Oops the third line should read
>0.999... - 0.999... = 0

that is pretty needless to mention. Only brainlet would mistake in believing that I meant + when I obviously meant -. Haha brainlets, when will they learn.

Rest of the argument is titanium proof.

Point is that if 0,999... = 1, then any number is actually any number

So if 0.999 = 1 is true
so is 3 = 4
so is -2 = 0
so is 2+2 = 9

It is infinity. Think about it, the smaller the numerator the larger the denominator so if the it's 0 then it must fellow that your mums a whore

>No matter how long I observe this pen on my table it remains the same!
>That must mean the pen WAS and always WILL be IDENTICALLY same

Your logic.

>any number is actually any number
no, x = x, y = y, x =/=y.

you're basing this on faulty logic and an inability for your feeble mind to comprehend working with numbers approaching.

just because you can't comprehend 0.999999999999999999999999999999999999999999999999999999999... ad infinitum does not mean it automatically rounds up to 1 in real world applications. your argument is shit.

0.9999.........8 =/= 0/9999......9 =/= 1

>titanium proof
what?

approaching infinity*

>1 - 9/10 - 9/100 - 9/1000... = 0
>(1 - 9/10 - 9/100 - 9/1000...) + (1 - 9/10 - 9/100 - 9/1000) + (1 - 9/10 - 9/100 - 9/1000) ... = 1
>0 + 0 + 0... = 1

there's no congruent logic between the last two lines. broken-rampant-in-post aside, if we play by your rules and say 1 - 9/10 - 9/100 - 9/1000 = 0. then your asserting that string would eventually regress to 0 on an infinite timeline and have no value to become additive on the timeline immediately following it. the logic is different between the first two lines and the last line, it doesn't make sense at all.

>Why isn't it infinity? Or 1?
it is, both, and every other number imaginable, or rather it COULD be any number. that's why it's undefined

What is the difference between 0.999...8 and 0.999...9? That's right. Zero.
What do we call two objects that have no differences? That's correct. Same.
What do we call two objects that have no no-differences? Indeed. Different.

Now if we have infinite amount of unique objects, whatever object you choose, there is always an object that is identically same to that object. By this logic, everyone of the objects is identically same.

Now imagine that for each of these identical objects you paint a unique number. Are the objects now different? No, because whenever you find any number, you are bound to find infinite amount of objects with the same number.

Now let's suppose I have infinity minus one objects, so a finite amount of objects. Now I will have 2 different objects! Because in the pool of objects there are at least two objects that I will not find infinite amount of identical pairs but only infinite minus one identical objects.

Zero, like infinity, is not actually a number. You cannot divide a non-number with another non-number because the operation of division is based on numbers.

Zero, like infinity, is not actually a number. You cannot multiply a non-number with another non-number because the operation of multiplication is based on numbers.

you are either autistic or don't understand the basic concept of mathematics.

infinite numbers means infinite possibility but not the possibility of repetition, that's a paradox.

the numbers are infinite, but there is only one 2, one 3, etc. not sure anyway to explain it in simpler terms, your logic basically just asserted numbers repeat on a finite timeline, which is downs tier. go back to /x, you don't understand basic mathematical concepts much less the rules for working with infinite numbers.

>What is the difference between 0.999...8 and 0.999...9? That's right. Zero.
the difference is actually 0.000...1, you can't round numbers to make them fit your bullshit logic, it doesn't work that way.

>Another 0.999... =! 1 crackpot

Please, to advance in mathematics we have to agree on some obvious, intuitionistic, very strong concepts like
>0.999... = 1

>inf means inf possibility but not the possibility of repetition, that's a paradox
Incorrect

Since 0.999... and 1 have no difference, we have two kinds of 1. We actually have infinite kinds of 1, infinite kinds of 2, infinite kinds of any number we can come up with. WE actually have infinite kinds of infinite kinds of infinite kinds of 1 etc. Every number has literally infinite descriptions in infinite dimensions, and each of those descriptions exist in infinite dimensions.

>infinite amount of unique objects
>whatever object you choose, there is always an object that is identically same to that object.

sounds like they're not unique objects in this example? are you counting fibonacci numbers or something, because numbers on a timeline from 0 to infinity do not repeat, that's a core concept of mathematics. it's not like saying "there are infinite pens and pencils in my desk. if i keep pulling them out one by one, i'll eventually find a duplicate."

>Now imagine that for each of these identical objects you paint a unique number. Are the objects now different? No, because whenever you find any number, you are bound to find infinite amount of objects with the same number.
not if you are counting from 0 to infinity. how fucking stupid can you be?

> if we play by your rules and say 1 - 9/10 - 9/100 - 9/1000 = 0. then your asserting that string would eventually regress to 0 on an infinite timeline and have no value to become additive on the timeline immediately following it.

This. Honestly 0.999.... = 1 absolutely makes you a crackpot, just accept that your theory is wrong, and move on. Stop polluting the thread with off topic nonsensical ravings like a lunatic please

en.wikipedia.org/wiki/0.999...
You do realize 0,999...= 1 is an accepted mathematical consensus amongst all prestigious and official Mathematical Institutions? I mean it's not my opinion man. It is as solid as 1+1 =2.

ACtually it can be very easily shown that if 0.999... =/= 1 then the whole quantum mechanical oscillatory wave of universe's wave function might collapse to singularity blackhole with infinite amount of regression!

New proofs have been formulated to show that 0.999... with non-infinite repeating decimals might ALSO be 1.

The numbers are unneeded, as the objects are already not identical due to their location in space. This entire thing is just shit posting, try to ignore this guy with his crazy "all numbers equal all numbers" malarchy.

>y 0/0 is undefined, user?
>derails into 0.999...=1 thread

absolut kek

This is why you won't ever contribute any significant scientific advance to Science.

You are bound by your intuition; the critical error in the brain of brainlets. You are like monkey contemplating that the things you see and feel must be real just because you feel that way!

No. Only mathematics can provide the absolute pure truth and whatever mathematics speaks must be true. Even facts like "all numbers equal all numbers". It is true, swallow it up and just marvel how amazing the world is.

>REEEEEEE IF IM WRONG THE UNIVERSE WOULD COLLAPSE INTO A BLACK HOLE
quantum mechanics is a fucking joke. doesn't it state the universe will collapse into a black hole anyway?? entropy must increase faggot. make your own thread you butt hurt autist. and take a course at uni while you're at it, you sound like a middle school education

>Entropy must increase
>Is an organism with entropy of -10^400

You fail to see the trees from the forest.

Also, what is the entropy of the number pi? That's right, negative infinity. So the existence of numbers like pi prove that your "entropy is always increasing in the universe hurr i just look at the sky with a telescope hurr im a physicists hurr spacetime is trampoline" is wrong. Hopelessly wrong. Desperately wrong.

You should leave these kinds of issues to mathematicians. You can focus on things like "is this bath water warm enough for humans" and "can i lift this stone?"

what are you talking about? are you just ranting now because you got shot down for being an autist? you said quantum physics first, and got cock slapped by it so don't be so butt hurt.

you still haven't been able to refute this
>if we play by your rules and say 1 - 9/10 - 9/100 - 9/1000 = 0. then your asserting that string would eventually regress to 0 on an infinite timeline and have no value to become additive on the timeline immediately following it.
no additive value of numbers regressing to zero.

get fucked dude, let us hear about your great "scientific advancement to science" you screeching autist. the only scientic community you're part of is the people on /sci who hate your thread hijacking ass apparently.

top kek. it really is too funny though this guy is just so mental i can't help but poke fun at him. it's like laughing at the kid who shit his pants in school; you feel bad for him in a way but can't help laughing at how hilarious it actually is.

this GED dropout isn't worth my time so i'll stop hijacking the thread. it's just so funny to read though

>(1 - 9/10 - 9/100 - 9/1000...) + (1 - 9/10 - 9/100 - 9/1000) + (1 - 9/10 - 9/100 - 9/1000) ... = 1
What?

Lets say it is 0/0 = 1.

then we have 5=5*(0/0)=(0*5)/0=0/0=1.

It is not infinity because infinity is not a number and if you add infinity to the real numbers it is not a field anymore.

Actually in this scenario you have provided an 'imaginary algorithm', or, 'alternate universe' where this has taken place.

0 = void|infinity
Humans really need to get that 0 is an ABSOLUTE starting point, not a RELATIVE one. 99.99% of concepts/objects are born of a 'relative' starting point + an absolute (0/infinity)

Aw, I was enjoying your posts. We could've been friends.

>0.999... + 0.999... = 0
>(1 - 9/10 - 9/100 - 9/1000...) + (1 - 9/10 - 9/100 - 9/1000) + (1 - 9/10 - 9/100 - 9/1000) ... = 1
Please kill yourself

In this instance I'd rather say 0/0 = 0^0 (intersection of infinity sets in a sense WEEEE)

0/0=x
0=x*0
x=any number
some people will take this to mean that 0/0=anything because you can put any number, but you only get any number because you haven't narrowed it down enough yet

if you do this one then you prove that 0/0 cannot be non zero:
0/0=x
2x0/0=2x
(2x0)/0=2x
0/0=2x
x=2x
1*0=2*0
x can only be 0
or rather x can't be non zero
perhaps there's something in the operation that makes it impossible to be 0 too
i don't really know maths at all

>having 0 friends
lls pathetic

0/0 = 0 * 0^(-1) = 0 * inf = 0

Someone actually took the time to proof my assertion. Sexy. That is one sexy thing to look at.

Why not utilize propto though instead of -1? Would make more sense and make the inf relational.

Make it purdy.

ITT: Kids that don't know limits.

If .999...=0
And .999...8=.999...
Then does .999...8=1?
Where does it stop?
Is .999...0=1?

1+2+3+4...=-1/12
0+1+2+3+4...=-1/12
(1+2+3+4...)-(0+1+2+3...)=((1-0)+(2-1)+(3-2)+(4-3)...)
(-1/12)-(-1/12)=(1+1+1+1...)
0=(1+1+1+1...)=(((math is a jewish trick)))
1+1+1+1...=infinity
0=infinity
infinity/infinity=1
0/0=1

checkmate atheists

woah...so this...is the power...of Post-Anabelian Froeboid Geometrics

(you could've just disproved the x=1 by using 0=x*0 instead)
Only sensible people in this ITT thread.

because theres a shit ton of functions who's limit evaluates to 0/0 but have different answers

If 0/0=x, then 0=0*x. Since x could be any number, 0/0 is not defined, for if it were, then every number would equal 1 or infinity or etc.

Because it depends on how you approach 0/0.
[eqn]\lim_{x \to \infty} \frac{c \sin{x}}{x} = \text{``0/0''} = c[/eqn]
[eqn]\lim_{x \to \infty} \frac{x^2}{e^x - 1} = \text{``0/0''} = 0[/eqn]
[eqn]\lim_{x \to \infty} \frac{\cos x - 1}{x^3} = \text{``0/0''} = \infty[/eqn]

Why not just cancel the zeros? That way you'll just get one.

Just cancel them out and you get one. You're allowed to cancel out infinities so why not zeros?

Jesus fucking Christ you niggers are fucking stupid. you don't need all these stupid fucking special equations you're all pulling out of your asses to find contradictions in math and the reasoning doesn't fucking depend on goddamn limits. read a middle school algebra book and learn about the fucking division algorithm.

Think about it, the limit of x/x approaching zero will always be one right?

x goes toward 0 in those

10*0.999...=9.99...
9.99-0.99...=9
if 0.999...=x
9.99...=10x
10x-x=9x
9.99...-0.99...=9x
9x=9
x=1
0.99...=1
but that means that
10x-x=8.999...
so 9x/9=0.9999...
so 1=/=0.999....

I'm gay and a C.U.C.K.

Nice digits.

Here are some disorganized intuition dickpumps for you.

------------------------------------

limit x -> 0 of x/x = 1

limit x -> 0 of 0/x = 0

limit x -> 0 of -x/x = -1

You see that approximations of 0/0 move towards different values if we inch towards them in different ways.

This should alert you that something is up.

------------------------------------

Or let's suppose it works to say 0/0 = 1 because 0*1 = 0.

If we accept that, we must also accept 0/0 = 2 because 0*2 = 0.

Therefore 1 = 2.

---------------------------------------

>If I ask my 0 friends over to eat out of my jar of 0 cookies, how many can each friend take?

The answer is not 1 each, or infinity each, the answer is "That doesn't make sense."

You sort of get two absolute starting points, the additive *and* multiplicative identities.

You can then use the distance between them as a way to talk about other values.

t. failed precalc

Whoops, yeah.

0 + 0 = 1

It took physical (pixel) matter to create those two zeros.

From a visual standpoint 0 + 0 = 1

From a conceptual standpoint 0 + 0 = 0

0/0 = -1/12

Proof: cross-multiply:
0*12 = -1*0
0=0
true

You might already have heard that 1/0=infinity.

For 0/0, there are many cases to be made, some of which already mentioned in the OP. You could say it's 1 because x/x=1 or you could say it's infinity or say it's 7. THAT is why it's undefined, because it's undefined which of them it is.

I will admit that I did once get roped into a pseudo-threesome with a drag queen and his boyfriend, but I chickened out because I just wasn't feeling it.

What's the acronym stand for?

0/0 is perfectly-well defined :
zero items divided into zero equal parts.
The Problem is that with zero equal parts,
you have no parts, therefore no division.
SO the problem is not one of definition,
it is a problem of operation, from which
you get no result.

From what I understand, zero has these problems:

1. 0 is undefined because any number works in place of whatever your variable is, i.e., 7, 21.05, -42^2, etc. I mean you can do what people were doing in the thread and you can see the equation makes no sense. I'm probably not explaining that right but whatever. See 4.

2. Your answer makes sense too.

3. 4. Approaching zero in different ways causes problems.

Those are just the ones mentioned in this thread.

It's 1.

Any other answer is wrong and they should feel bad about not knowing math.

People should stop treating 0 as, 0=infinity.

It's wrong.

UNDEFINED

People here should spend less time browsing Veeky Forums and more time studying.

Zero doesn't exist.

Any math using zero is a fucking cop-out

I recently read somewhere that the old greeks or arabs or whatever didn't even consider 1 a number. Maybe it was bs, sounds pretty stupid now that I think about it.

You should get better at math. It could pay off one day.

1/3 = 1/3
1/3 = .333...
1/3 + 1/3 = 2/3
1/3 + 1/3 = .666...
1/3 + 1/3 + 1/3 = 3/3 = 1
1/3 + 1/3 + 1/3 = .999...