Re: how

Le 14/06/2024 à 20:52, Jim Burns a écrit :

On 6/14/2024 12:39 PM, WM wrote:

every number in {i:∀₃Xᴬ⤾⁺¹₀:X∋i}
has ℵ₀ successors in {i:∀₃Xᴬ⤾⁺¹₀:X∋i}
 

Note that
only the numbers with successors are deleted,
the successors remain by definition.

 sⱼ∘f:{0<} → {j⁺¹<}  is 1.to.1

If only numbers having ℵo successors are removed and only as long as ℵo successors remain, then ℵo successors remain and every definable number is removed. You cannot defina a number that remains. But ℵo successors remain
Regards, WM