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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.They are no finite.
You can't believe Z_0 to be "complete" inThey are minutely equivalent. To described both take ℕ. Delete 1. If you have deleted n, delete n+1. In all steps ℵ₀ numbers remain.
your sense if you don't think the second set is (and accept that they
are equivalent).
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