Why is dividing by 0 not infinity? Wouldn't 0 go into any number infinitely many times...

Why is dividing by 0 not infinity? Wouldn't 0 go into any number infinitely many times? I can see why 0/0 might be undefined since there is an ambiguity between an answer of 1 and infinity but for any other number wouldn't infinity be an acceptable answer?

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>but for any other number wouldn't infinity be an acceptable answer?
But this "answer" is just as crappy as saying it's not defined. Since all numbers give the same result when divided by zero you can't solve equations or do anything useful. May as well say 1/0 = wumbo

If division by zero is permitted then you can easily "prove" 1=2 and other nonsense.
So it's a "forbidden operation".
You CAN say that as X approaches zero, 1/X approaches infinity. That's legal. It took a couple of centuries after Newton to put the calculus on a firm enough footing that it could handle such issues.

1/0 = infinity in projective space. This makes perfect sense but it is incompatible with some other laws of arithmetic.

How many times do you have to multiply 0 by itself to get 1? Infinity? Are you sure? If you concede that 0^n=0 for any n, then you can't argue 1/0 is anything at all

>Why is dividing by 0 not infinity?
It's undecidable because it approaches either positive or negative infinity depending on which way you approach the limit.

Actually you would be adding 0 to itself, not multiplying.

>1=2
Why

Yeah my mistake, realized after I posted

WUMBO
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mathforum.org/library/drmath/view/57116.html

>Why is dividing by 0 not infinity?
In which wheel?

could you make a wheel with a congruence class?

>could you make a wheel with a congruence class?
What do you mean?

idk lol
I'm trying to come up with a wheel but i don't know anything about wheel theory
The only thing I came across with different operations are congruences
Could you just replace division with factorial or does that not satisfy the axioms?

>I'm trying to come up with a wheel but i don't know anything about wheel theory
Any commutative ring can be extended to a wheel

Google complex infinity, or point at infinity.

Simple thought experiment
Take one cake.
Cut it into zero pieces.
How many pieces do you have?

Take one cake. Cut it into 0.1 pieces.

0 pieces imply that the cake shouldn't exist at the end, so you smash it so hard that it breaks into an infinite amount of nonexistent parts.

Ok I've got one slice of cake out of ten in my hand. Now what?

You just said to cut it into 0 pieces, so obviously you're going to have 0 pieces

Once you allow x/0 make sense in the same sense as x/(non-zero number) then everything else loses meaning. Every value is now both zero and infinity. You've done fucked yourself now.
look at dis:
2/0 = Inf
3/0 = Inf
2/0=3/0
2=3=4=5=9.1312=9x10^1391

And then you start believing there are infinite genders and you're lost forever.
If you have x approach zero like so: 1/x You can approach either infinity or negative infinity depending on which side of the number line you approach from.
I'm very certain of how uncertain I am about understanding this concept, I've just been thinking about it a lot the past few months.
There are limits in mathematics like there are in anything. If there were not then nothing would be of any worth.
If anything is infinite then everything is infinite. If nothing is infinite then nothing is finite. idk man just keep living and stuff this shit confuses the hell out of us all I'm pretty sure

A/B = C
6/2 = 3
6/0 = inf

C*B = A
3*2 = 6
Inf*0 = 6????

So the whole cake was one piece?
How would you cut a cake into two pieces?
Bake another one?

for any number x, you look at 1/x as the number that gives x* (1/x) = 1
then any fraction a/b is simply a times 1/b
since 0 times anything is equal to 0, you can't have a 1/0, or anything else divided by zero

because infinity*0 is undefined you dumb fuck

What if I upgrade to tank treads?

division by 0 equals x + x
[math]x/0 = y[/math]
[math]x = 0y[/math]
[math]x = 0* x + x[/math]
[math]x = x[/math]

-1/12

I thought we were in agreement that it approaches infinity and negative infinity?

a/0 = infinity

What this means is that there is a if you multiply 0 infinity times you get a.

Which means that 0 * a, as a -> infinity, 0 * a should as well, but the derivative of 0 * a is zero, so no matter how big you make a, it wont make f(a) anything other than zero, even as a goes to infinity.

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>Why is dividing by 0 not infinity?
Because it is not defined.
Because infinity is not a number (an element of R).
Because wheel theory is not all that useful.

>for any other number wouldn't infinity be an acceptable answer?
No.