Re: The set of necessary FISONs

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. In any case,
the second set does not exist according to your contradictory specifi-
cation. They are clearly isomorphic.


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Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.