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Subject: Re: Does the number of nines =?UTF-8?Q?increase=3F?=
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Le 26/06/2024 à 00:11, Jim Burns a écrit :
> On 6/25/2024 4:18 PM, WM wrote:
> 
>> Let the infinite sequence 0.999...
>> be multiplied by 10.
>> Does the number of nines grow?
> 
> Cardinalities which can grow by 1 are finite.
> The number of nines in 0.999... is
> larger than each finite cardinality.
> It does not equal any finite cardinality.
> It cannot grow by 1
> 
> tl;dr
> No.

Is the set of natural indices complete such that no natural number can be 
added?

> Nuance:
> There are _only_ positions in 0.999... which
> are separated by some finite number,
> even though there are infinitely.many of them.
> 
> The positions in 0.999... correspond to
> numbers in well.ordered inductive ℕᴬ⤾⁺¹₀ᐣ⤓

And they are fixed. Therefore your answer is correct:No. Therefore 
9.999... has one 9 less after the decimal point than 0.999... .

Regards, WM