[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

A way to prove numbers are unbounded is through proof by contradiction. Let’s assume that an upper bound to numbers exists and that upper bound is B. We can then add 1 to B, so that upper bound is now B+1. We can then wash, rinse, repeat. So, numbers are unbounded.