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I know that 0/any number=0 and any number/0=no answer, (negative) infinity, undefined. So, what happens if we divide zero by itself? Is it zero? Is it infinity? Well, infinity isn't a real number, but let's cut to the real chase. Let's say there are two points on a coordinate plane put together. How will we know what line to draw? What slope does it have? We know that the x- and y-intercepts are the same. What happens when we divide zero by zero?

VladInTheTaylor
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  • Divsion by zero is not defined because zero does not have a multiplicative inverse. It follows from the ring axioms that $0x=0$ for all $x\in \mathbb{R}$ and therefore there is no $y\in \mathbb{R}$ such that $0y=1$. – Seth Dec 13 '14 at 15:12
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    The universe implodes into itself. Don't try it! – Timbuc Dec 13 '14 at 15:12
  • I don't care... – VladInTheTaylor Dec 13 '14 at 15:13
  • The derivative in calculus is all about dividing tiny things by tiny things, in the limit as the tiny things become zero. – Empy2 Dec 13 '14 at 15:14

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0/0 is undefined, but if you want a value, this is best done using limits. 0/0 can be approached in multiple ways.

First of all, there is the function x/x. The limit of this function as x goes to 0 is 1.

There is also 0/x, the limit of this function as x goes to 0 is 0.

And the last one I will discuss: x/0 as x goes to 0. This limit does not exist.

Of course, you can think of many more limits.

Dasherman
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    There is also $(\sin x)/x$ which approaches 1 if you use radians, or $\pi/180$ if you use degrees. – Empy2 Dec 13 '14 at 15:24
  • Yup, I personally like that limit a lot. Limits really are full of surprises. There is of course an infinite amount of limits we can think of to approach the problem of 0/0, but I just listed the three first ones I thought of. – Dasherman Dec 13 '14 at 15:27