Re: The set of necessary FISONs

Am Wed, 12 Feb 2025 10:25:32 +0100 schrieb WM:

On 11.02.2025 21:01, joes wrote:

Am Tue, 11 Feb 2025 10:31:48 +0100 schrieb WM:

 

The set F of FISONs which can be removed without changing the assumed
result UF = ℕ is the infinite set F of all FISONs. This is proven by
just the same induction as Zermelo proves his infinite set Z.

Nope, any *finite* set of FISONs can be removed. The set of *those*
is infinite, but no set of removable FISONs is.
(Zermelo or whoever don’t prove the membership of infinite elements.)

Zermelo proves the existence of the set Z which contains the infinite
set ℕ of all finite natural numbers.

Pretty sure he doesn’t. What else is in Z?

I prove the existence of the infinite set F of all finite FISONs
removable without changing the result of UF.

No, if you remove everything, you change the union. The union of
all FISONs is not empty.
You only prove that it doesn’t matter *which* single FISON you remove.
You don’t even talk about more than one. If you tried, you’d get
*sets of* FISONs.

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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.