[henry2023]

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,_%...

[topaz0]

"_____ is not defined anywhere in math"

is a kind of sentence that is almost never true, and even if it were, it would be impossible to prove that someone hadn't jotted a valid definition on a napkin somewhere. In this case it is certainly not true (as others have mentioned: https://en.wikipedia.org/wiki/Riemann_sphere ). Now, specifying a definition for division by zero does require you to be careful about how the other operations extend to this new number, but there are perfectly consistent (and useful!) ways to do so.