[yodsanklai]

> But there is no such distinction

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

[constantcrying]

>Of course there's a distinction. A decimal representation is a sequence of digits, not a number

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.