Sorry to be a bitch, but anything (except zero) divided by zero is undefined. Zero divided by zero, on the other hand, has its own special term.

It is not undefined, but indeterminate.

In reality, you can pull all sorts of crazy shit with infinity. Infinity divided by infinity, for example. Anything divided by itself is one, right? Wrong. Any real number divided by itself is 1. And infinity is unfortunately not a real number.

Picture this. There are an infinite number of ways this writeup could be cooled. Someone could do the honours, or the system could go haywire, or God Himself could do it, or...Also, there are a infinite number of Universal possibilities: eg, this writeup could turn into a butterfly and fly off my monitor.
Thus, the probability of this writeup being cooled is infinity on infinity. If this is equal to one, then I'm guaranteed a cool! I wish. :)

Conclusion: Zero on zero is indeterminate. Infinity is not a element of the reals.