Of course there's a distinction. A decimal representation is a sequence of digits, not a number
> Why?
It boils down from the definition of the decimal representation and the limit of a geometrical sequence.
https://en.wikipedia.org/wiki/Decimal_representation
Oh and what is a real number? Might a real number be a sequence of rationals? Or more correctly an equivalence class of cauchy series.
>It boils down from the definition of the decimal representation and the limit of a geometrical sequence.
No, it doesn't. You are assuming the conclusion.
