Re: how

Le 12/04/2024 à 15:58, Richard Damon a écrit :

On 4/12/24 9:40 AM, WM wrote:

Le 12/04/2024 à 00:32, Richard Damon a écrit :

On 4/11/24 8:03 AM, WM wrote:

Le 11/04/2024 à 01:04, Richard Damon a écrit :
>

Except that there *IS NO* Natural Number with less than ℵo successors,

>
That is wrong if/because *all* natural numbers have no successors.

 {1, 2, 3, ...} there are no successors. But every useable number has ∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo successors.

  Why do you say there are no succesors. As you say, for EVERY Natural Number there are ℵo successors

No, only for every definable number. Between ℕ and ω there is nothing.

 Even for all the numbers in the ..., as it NEVER ENDS and thus EVERY value in it still has ℵo successors.

Beyond ℕ there is none.

 

>
How do you expect to index an infihite set with finite operations.

 I don't. Matheologians do.

 Then why do you talk about a set of Number you "don't believe" in?

I believe in the complete set which ends before ω.

You can't talk about "Cantor" and his bijections, if you don't accept the rules he discussed his theories in.

He erred.
Regards, WM