Re: The set of necessary FISONs

Am Mon, 10 Mar 2025 16:20:58 +0100 schrieb WM:

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

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

No, they are not finite. You can't believe Z_0 to be "complete" in
your sense if you don't think the second set is (and accept that they
are equivalent).

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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.