Re: Does the number of nines increase?

Am 11.07.2024 um 00:28 schrieb Chris M. Thomasson:

Think of the whole as simply, sqrt(2)

It's possible to "construct" the real numbers that way.

The finite parts are the step wise construction of the whole, can be something akin to:
 (1, 1.4, 1.41, 1.414, ...)
 Is this a decent line of thought?

Yes.
Cantor "constructed" (defined) the real numbers "that way" (or in a "similar" way).
Hint: There are quite different "constructions" of the real numbers (Dedekind, Contor, ...) but all these "constructions" lead to "the same" (up to isomorphism) "field" called "the real numbers".