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Subject: Re: Does the number of nines =?UTF-8?Q?increase=3F?=
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From: WM <wolfgang.mueckenheim@tha.de>
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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