Re: Does the number of nines increase?

Am Sun, 30 Jun 2024 15:18:31 +0000 schrieb WM:

Le 29/06/2024 à 22:25, joes a écrit :

Am Sat, 29 Jun 2024 17:18:26 +0000 schrieb WM:

 

All nines of 0.999... are from the sequence 0.9, 0.09, 0.009, ... None
of the ℵo nines makes its partial sum 0,9, 0.99, 0.999, ... equal to
1. ℵo nines fail to make 0.999... = 1.

That’s one way to construct it. Of course none of the infinite series
individually reaches the limit (otherwise the following ones :-P would
go above it?). Together they do. It is reached after exactly Aleph0
steps.

Which is to say, after all of the steps.

Are there ℵo partial sums 0.9, 0.99, 0.999, ... ?
If yes they can be combined to 0.999... .

That is the limit, yes.

Is the limit one of them?

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Am Fri, 28 Jun 2024 16:52:17 -0500 schrieb olcott:
Objectively I am a genius.