Re: because g?(g?¹(x)) = g(y) [1/2] Re: how

WM explained :

Le 08/05/2024 à 23:55, Jim Burns a écrit :

On 5/8/2024 3:55 PM, WM wrote:

Le 07/05/2024 à 00:11, Jim Burns a écrit :

 

All which canNOT be counted.to are not.in ℕ

>
All which canNOT be counted.to are not.in ℕ_def.

 And all which CAN be counted.to are in ℕ_def.

>
Yes. But every n ∈ ℕ_def has ℵ₀ successors which never vanish by counting. They can be removed only collectively such that nothing of ℕ remains.

Wrong, but you can remove any, each, every, or even all from consideration in building a *NEW SET* because *SETS DON"T CHANGE*.
Such new set may be finite, or not, and be a proper or improper subset of the still *UNCHANGED* superset.