Re: Does the number of nines increase?

On 6/30/2024 8:18 AM, WM wrote:

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.

 Are there ℵo partial sums 0.9, 0.99, 0.999, ... ?
If yes they can be combined to 0.999... .
Is the limit one of them?

The limit is one. This is how many calculators in base ten can represent one:
1 = .(9) = (.999...) = 1