Re: Does the number of nines increase?

Le 29/06/2024 à 15:24, Jim Burns a écrit :

On 6/28/2024 9:50 AM, WM wrote:

It is changing the infinite set
but not its cardinality.

 A set with a cardinal.growable.by.1 (finiteⁿᵒᵗᐧᵂᴹ)
cannot change without its cardinality changing.

Cardinality is irrelevant.

Therefore cardinality is useless for my proof.

For any difficulty which cardinality presents,
not.saying 'cardinal' not.resolves the difficulty.

Cardinality does not present a difficulty. It is simply unable to distinguish |ℕ| and |ℕ_0|.
All nines of 0.999... are from the sequence 0.9, 0.09, 0.009, ... None of the ℵo nines makes its partial sum 0,9, 0.99, 0.999, ... equal to 1. ℵo nines fail to make 0.999... = 1.
Regards, WM
 Regards, WM