is there any way to validate the fact that if a function is 1-1 and onto, then it is invertible using a proof?

Question

or has nobody been able to rpove it yet and its just one of those things that is accepted because nobody has disrproved it? Plz Help!

Answer 1

It's trivial from the definitions.

For any y, by the definition of onto there's at least one x such that f(x) = y. By the definition of 1-1, that x is unique. So map y to that x.

That's your inverse function.

It's really that easy.

I imagine that one can come up with some mumbo-jumbo about how the Axiom of Choice is concealed in there somewhere -- but unless you're pretty far into a university math major, don't worry about that at all.