Re: how

Le 22/06/2024 à 23:25, Jim Burns a écrit :

On 6/22/2024 4:23 PM, WM wrote:

IF ℕ is the union of FISONs,
THEN ℕ is empty.
ℕ is not empty.

 IF ℕ is the union of necessary FISONs,
THEN ℕ is empty.
ℕ is not empty.
ℕ is not the union of necessary FISONs,
 ⎛ No single FISON is necessary.
⎜ Even! No _finite_ FISON.subset is necessary.
⎝ The whole infinite FISON.set is necessary.
 

No. What a pathetic statement. The first 10^100000 FISONs are not necessary.
Every existing set of ordinals has a first or smallest element. The set of FISONs necessary to yield ℕ would be a set of ordinals. It is well defined since for every FISON we can determine whether it is necessary. It has no smallest element. ==> It is empty.
Regards, WM