[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

Some maths doesn’t change as the numbers get bigger. So as an example, for a function f(x) – meaning we put in any number x and get a result f(x) – if we can show that f(x+1) is bigger than f(x), then we know that f(x) goes to infinity as x gets larger.

When you start to tie the maths to physical objects, that’s when things get complicated.