@demofox @bnut
One important thing (even in other philosophies of mathematics) is that the decimal expansion of a number isn't really the same as the number itself. It is merely an infinite series that converges to the number that we have built a convenient shorthand around, but just like 1/2 = 2/4 is the same number, with a different notation, we have things like 0.999… = 1, since 0.999… is just a shorthand for sum_{k=1}^inf 9*10^(-k), which converges to 1.

As such, you can reason about e.g. pi, without ever computing all its digits. For example, in university, we just proved that 3 < π < 4 and called it a day, it's good enough.