That might be a silly question, but here goes: I see a lot of "big numbers" in physics, such as the size of the state space of all the particles in the visible Universe, and those numbers can be written down, like $10^{10,000}$, or whatever that particular value turns out to be. Maybe there comes a time where we couldn't even write down a large number, because we wouldn't have enough atoms in the Universe. At that point, we might resort to a program or a sentence to describe how to compute the number that we could never actually write down. Then maybe we could get to an even larger number that can't even be described with any program or sentence, not even in principle? Is there such a number?
2026-04-03 01:40:39.1775180439
Question about infinity
304 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
If you have a fixed set of symbols, and set a bound on how many characters you are allowed, then you can only distinguish a finite number of numbers. Since the observable universe is finite, you can only use atoms in the universe to distinguish a finite number of numbers. So, yes, there are an infinite number of numbers that cannot be explicitly specified in a way that distinguishes them from all other numbers. And we're not even talking about classes of infinity here, just finite numbers that there aren't enough atoms to describe.
There are paradoxes about writing down the smallest such number, and that's an interesting topic. But the fact is, most (all except for finitely many) numbers are just too big to write down.