Re: Does the number of nines increase?

Le 30/06/2024 à 19:56, joes a écrit :

Am Sun, 30 Jun 2024 14:51:42 +0000 schrieb WM:

Le 30/06/2024 à 12:29, Jim Burns a écrit :

 

The values of infinite length decimals are assigned by a different
method from how the values of finite length decimals are assigned.
0.999...  ≠  0.99999  <  1 ...

 If you use only definable length, then always ℵo terms are missing.

Did you mean: /finite/ length ?

Only finite length is definable.

All finite indices guarantee finite length.

 0.(9) is not finitely long though, so there are no „missing” terms
 

0.9 + 0.09 + 0.009 + ... contains ℵo terms with ℵo nines, all together
smaller than 1.

We are not talking about the terms, but their limit,

which is not reached by any of the ℵo partial sum.

which is all of them
/taken together/.

Nonsense. Show any terms which taken together are larger than all singles.
Regards, WM