>>11570021Yes. The problem here is your definition of division is not the usual one. Usually what's done is this:
Axiom 1: There exists a number, denoted by 1, such that for any number a, a * 1 = a.
Axiom 2: For every number a ? 0, there exists a number, denoted by a^(-1), such that a * a^(-1) = 1.
Definition 1: a / b is the same as a * b^(-1), with b^(-1) defined above.
Under these conditions, 0 / 0 means 0 * 0^(-1), and 0^(-1) isn't a defined object, it's the same as just squiggling in your paper.
However, I think what you're asking is "Why can't we just change the axiom 2 and make it so 0 can have a multiplicative inverse?" Ok, let's do that. Now 0 / 0 is 0 * 0^(-1), which by definition of what 0^(-1) means, has to equal 1. And you can see how this leads to contradictions when you try to evaluate 10 * (0 / 0) = (10 * 0) / 0, for example. The left-hand side is 10 and the right-hand side is 1. So to avoid this contradiction we'd need to make it so multiplication isn't associative anymore, which ok, we can do, but is kinda retarded.
The point I'm trying to make is you should write down your definitions for multiplication and division, and see how you can arrive at 0 / 0 = 1 in a way that doesn't contradict anything you wrote down. You'll probably run into trouble because 0^(-1) will be something that you can multiply by 0, but can't multiply by any other number, which means it's kinda useless.
