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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: The set of necessary FISONs
Date: Sat, 1 Feb 2025 13:46:50 +0100
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On 31.01.2025 18:51, joes wrote:
> Am Fri, 31 Jan 2025 13:28:35 +0100 schrieb WM:

>> then all can be discarded,
> No, only finitely consecutive ones.

Induction concerns all natural numbers n as well as all A(n).
> 
>>>> But all F(n) can be shown to be completely useless because infinitely
>>>> many natnumbers are missing.
>>> Again: every single one, or even an arbitrary finite number.
>>> If you have inf. many segments, you obviously have inf. many numbers.
>> All finite natural numbers as well as all FISONs obey the Peano axioms.
> All naturals are finite. FISONs are not naturals but sets and can’t be
> added together.

FISONs represent ordinals.
> 
>> Removing all leaves nothing, in particular no sufficient set for
>> U(F(n)) = ℕ.
> It is obvious that N is not empty.

But the set claimed to have the union ℕ gets empty without changing its 
union.

Regards, WM