[ELI5] how do we prove that something goes to infinity or – infinity since we can’t observe it?

Question

For instance how do we know that something weird doesn’t happen at some insanely large number?

In: 3

Answer 1

Mathematical proofs aren’t observational. We know it because we can prove it, using the definition of a limit. Yes, we can often take a good guess based on observations, but that’s not a proof.

The definition of a limit itself is pretty formal, and a bit hard to ELI5. But it is a definition, and you can prove that a certain function meets the definition.