The key point here is that you shouldn't be thinking of counting as a process that happens in time. How is infinity (here, omega) defined? We just say that it comes after any other natural number. So how to think about it? You shouldn't tell yourself:
- ok, take number n, it's smaller than omega, so what about n+1, n+2, etc. ?
You should be telling yourself
- ok, take number n. It's smaller than omega. Now check any other number m. If this property holds for any given number, then omega is greater than any given number, and thus infinite.
- ok, take number n, it's smaller than omega, so what about n+1, n+2, etc. ?
You should be telling yourself - ok, take number n. It's smaller than omega. Now check any other number m. If this property holds for any given number, then omega is greater than any given number, and thus infinite.