[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

In mathematics something goes to infinity if you can choose any number you like, and it goes bigger than that.

So like y = x squared. It goes to +infinity because if you pick a number, like 10000, I can pick a number like 101 and 101 squared is bigger than 10000. So then you say 1,000,000 and I say 1,001. then you say 999,999,999,999,999 and I say 999,999,999 squared is bigger. No matter what you pick there’s a number that’s bigger when you square it.

It doesn’t go to -infinity though, because if we do the opposite, it doesn’t work. If you say 5 I say 2 squared is lower than 5. But if you say -1 I’m stuck because you can’t square anything and get a number lower than -1. (we’re not doing imaginary numbers)