Re: The set of necessary FISONs

Le 10/03/2025 à 09:30, joes a écrit :

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

On 09.03.2025 17:26, Jim Burns wrote:
 

You even avoid hearing what we mean.
 

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