Re: The set of necessary FISONs

On 10.03.2025 09:30, joes wrote:

Am Sun, 09 Mar 2025 20:13:53 +0100 schrieb WM:

I am interested in the difference that you see between
>
Z₀ defined by { } ∈ Z₀, and if {{{...{{{ }}}...}}} with n curly brackets
∈ Z₀ then {{{...{{{ }}}...}}} with n+1 curly brackets ∈ Z₀
>
and
>
The set of FISONs failing to have the union ℕ defied by induction:
|ℕ \ {1}| = ℵo, and if |ℕ \ {1, 2, 3, ..., n}| = ℵo then |ℕ \ {1, 2, 3,
..., n+1}| = ℵo.

 How you can view the first set not to have the same union (by Neumann's
equivalence) as the the second one would be most welcome.

That is no my opinion but Jim Burns' opinion.
Both sets are identical. Both are potentially infinite collections.
Regards, WM
Regards, WM