The Switch Between Finite and Infinite?

A in comminatoric, we don't really think about infinite things. We would say there's just some finite number of things that can happen and maybe we can count them all. A lot of computations are done like this, right? If you ask, well, fermelfa, give me a limit as something goes to infinity, it doesn't actually do that. It comes up with some finite way of approximating it, and then it tells you that number. But how would the system be infinite in the first place, if you can make it finite? No, no, i'm saying instead, take the same thing to n, make the system for n, marg