Comment by nilkn

> Maybe you were able to cut at 10.000, but if you go more precise you'll start seeing other digits, and they will not be repeating. You just picked a real number.

A reasonably defensible inference would be that adding a finite amount of precision adds a finite number of additional digits. That is a physically realizable operation. There's no obvious physical meaning to the idea of repeating that operation infinitely many times, so this is not clearly a meaningful way of defining or constructing real numbers. If you were trying to use this construction to convince a skeptic that irrational real numbers exist, you would fail -- they would simply retort that arbitrary finite precision exists and that you have failed to demonstrate infinite non-repeating, non-terminating precision.