Re: Does the number of nines increase?

WM explained :

Le 26/06/2024 à 20:46, "Chris M. Thomasson" a écrit :

On 6/26/2024 12:15 AM, WM wrote:

>

9.999... has one 9 less after the decimal point than 0.999... .

 NO! Think of: .(9) * 10 = 9.(9) = 10

>
Wrong.
>
10*0.999...999 = 9.999...990
>
==> 10*0.999...999 < 9.999...999
>
==> 9*0.999...999 < 9
>
==> 0.999... < 1
>

There are still infinite nines... :^)

>
If the set ℕ is actually complete, then the set ℕ_0 has one element more.

If by 'complete' you mean something entirely different from what it means to most of the rest of the posters here. The set of naturals is 'complete' in your sense because it is defined such that it contains *all* of its elements. All sets are 'complete' in that sense.