A recent post asked:

What does it mean to divide by zero? In mathematics, this operation is undefined.

Back up the wagon, Chester! We first need to clarify: in which number line?

In the natural and relational number lines, the two integer lines we are mostly familiar with, "undefined" is probably the correct answer. I say "probably" because the history of mathematics is littered with the corpses of "undefinables" which subsequently proved to be definable.

In the hyperreal number line, it's wrong. In this line, 0 is one of the possible values of h, which is defined as a number which, for all values of n, is greater than -n and less than n. From this it follows that any number divided by 0 equals infinity, because 0 is a non-finite value equal to every other value within h. And thereby the calculus is made respectable.