Re: how

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

>
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?
Any time you mention "Natural Numbers", or "ℵo", you are accepting the "Mathology".
You can't talk about "Cantor" and his bijections, if you don't accept the rules he discussed his theories in.
You just seem to be too stupid to understand that fact.
You logic only handles FINITE sets (possible of unspecified by finite size), as such, "infinte" bijections can't occur, so you can't talk about the mapping of N to NxN as you don't HAVE the set N.

 Regards, WM