Division by zero is not defined anywhere on math.

The closest thing you'd get to it is to

1. define a limit (lim x->a of ƒ(x) exists if and only if given any ε > 0 there exists a δ > 0 such that ...)[1].

2. chose a function ƒ(x) such that on a given "a", ƒ(a) = ƒ(a)/0.

3. prove that the limit exists and is finite.

Now if we defined division by zero it would look like this:

Axiom: For every element x of the real numbers there exists a x' in the real numbers such that x/0 = x'

I advise you to play with this new "rule" to see if it leads to something interesting. Hint: try to prove that 1/0 = 2/0

[1]: https://en.wikipedia.org/wiki/Limit_of_a_function#(%CE%B5,_%...