Re: how

Le 14/06/2024 à 16:56, Jim Burns a écrit :

On 6/14/2024 4:34 AM, WM wrote:

Le 13/06/2024 à 20:25, Jim Burns a écrit :

On 6/13/2024 10:55 AM, WM wrote:

 

Every number has ℵo successors.

 Yes.

No. Here is the context:
WM: If every number is subtracted, then no successors remain.
FF: Eine wirklich bemerkenswerte Erkenntnis!
WM: It contradicts your claim that every number has ℵo successors.
FF: No, WM (Proof by contradiction): Every number has ℵo successors.
If every number is subtracted the successors remain.

You:

Every number has ℵo successors.

In a proof by contradiction.

 

If all numbers which have ℵo successors
are deleted from ℕ,

 ...and

Every number has ℵo successors.

 

then ℵo successors remain in ℕ

 ...then successors which haven't ℵ₀ successors
remain in the new not.ℕ set.
That is 0 successors.

That are infinitly many successors.
Note that only the numbers with successors are deleted, the successors remain by definition.
 Regards, WM