Re: Does the number of nines increase?

Am Sat, 29 Jun 2024 17:18:26 +0000 schrieb WM:

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 (finite)
cannot change without its cardinality changing.

Cardinality is irrelevant.

Then how do you measure infinite sets?

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|.

Working as designed. How do you distinguish them?

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.

That’s one way to construct it. Of course none of the infinite series
individually reaches the limit (otherwise the following ones :-P would go
above it?). Together they do. It is reached after exactly Aleph0 steps.

--
Am Fri, 28 Jun 2024 16:52:17 -0500 schrieb olcott:
Objectively I am a genius.