Re: Does the number of nines increase?

On 7/1/2024 10:24 AM, Moebius wrote:

Am 01.07.2024 um 18:37 schrieb Chris M. Thomasson:

On 7/1/2024 9:15 AM, WM wrote:

Le 30/06/2024 à 20:45, Moebius a écrit :

Am 25.06.2024 um 22:18 schrieb WM:
>

Let the infinite sequence 0.999...

>
0.999... ist keine "infinite sequence", sondern eine Zahl,

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Wrong. 0.999... is an abbreviation of ...(((0.9)9)9)... = 0.9, 0.99, 0.999, ... converging to but never reaching 1.
>

.(9) is just <etc.>

 Please don't make the same mistakes as Mückenheim.
 I'm talking about the number 0.999... (i.e. 1) here.

.999... = .(9) = 1
That is just how base 10 can represent one, rather than just 1.
1 = .999... = .(9) = 1
Fair enough?

Not about the string "0.999..." (consisting of 8 characters) or a "representation" (say the decimal representation) of the number which may be denoted by the string "0.999...", or ".(9)", etc.

Not about storing the individual iterates as in using memory for each iterate. We can compute them, and gain a precision, say a fractal needs enough nines to render itself.
.0010105599999999
Works, The number of 9's is there, it is a finite view.
.00101055999999999 is a completely different fractal.

 This means especially that 0.999... (i.e. the number 1) is not an "infinite sequence".