Re: Does the number of nines increase?

Le 03/07/2024 à 23:30, Moebius a écrit :

Wir definieren eine "non-terminating digit sequence" the following way:

Defining and writing are different.

 Wir betrachten die Folge (d_n)_(n e IN), die durch d_i = 3 für alle i e IN definiert ist.

That is a formula. The formula defines every digit of the infinite sequence and its limit.
It is impossible to define the formula or the limit by an infinite sequence.

 Diese Folge "determiniert" die reelle Zahl SUM_(n=1..oo) d_n/10^n = 1/3.
 

No. The formula defines the sequence. An infinite sequence has infinitely many digits which are given, not only abbreviated by a formula. This is a formula: "0.333...". Like any other infinite sequence this infinite sequence cannot be given.
Regards, WMK