filtherton

1/0 is undefined. It is undefined because no one has yet thought up an agreeable algebraic way to describe what happens when you divide by zero in any kind of meaningful way. It just doesn't work. Even if you multiply zero by infinity you'll never get a product other than zero. If someone figures out a useful way to define it it will be thusly so. Until then it's just a big no-no.

Limits are useful because they describe what happens near a certain point - what actually happens at that point isn't very important as far as the limit is concerned. The limit of 1/x as x approaches 0 is infinity. 1/0 is undefined. This is a crucial distinction to make. What's kind of more interesting is that you can take the limit of, say x*e^(-x) as x approaches infinity. Evaluating it as you would a continuous function gives you infinity/infinity. How you explicitly evaluate a limit like this is a calc 1 kind of thing. In this case since the e^(-x) term increases in magnitude much faster than the x term the actual limit is zero.

Mathematical operations are reversible. I think what that really means is that if you can get to a from b you should be able to get back to a from b. However, dividing by zero gives you a number that is undefined, which is basically another way of saying "We don't know what the fuck to do with that so let's make an exception out of it". Algebra is good for a great many things, division by zero is not one of them. Calculus, in my experience does little to shed light on division by zero, but they give you other things to think about.

I may be wrong though, i'm no math teacher.