Re: Does the number of nines increase?

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 ?

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 all of them
/taken together/.

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