Re: Does the number of nines increase?

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