[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

I’ll try and give a simple example:

Let’s start at the number 2. Then we add 2 and get to 4. Then we add 2 again and get to 6, then to 8,10,12 etc. Then we add 2 again and again and again. We can do that “to infinity”.

Every single number we will ever get to will be even. I am very sure nothing “weird” will happen at “some insanely large number”.

Other sequences that go to infinity like this one have similar, although probably more complicated, rules. And from these rules we can infer all kinds of patterns and other rules, even though we can practically only observe a minuscule fraction of infinity.