Someone has never explained to me why you can't divide by 0. Wouldn't 1/0=infinity?
The limit of 1/x as x approaches 0 from above is infinity. The limit as x approaches 0 from below is negative infinity. (This is on R union {-infinity, infinity} by the way.) Since the answer is different depending on which direction you approach from, the plain non-directional limit is undefined.
There is another formulation of this that treats R union {infinity} as topologically equivalent to a circle, so that negative infinity equals infinity. In this case, anything (except 0) divided by 0 can be well-defined as infinity. If you don't explicitly make that assumption, though, it doesn't necessarily work.