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From: joes <noreply@example.org>
Newsgroups: sci.math
Subject: Re: The set of necessary FISONs
Date: Sat, 1 Feb 2025 14:07:28 -0000 (UTC)
Organization: i2pn2 (i2pn.org)
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Am Sat, 01 Feb 2025 13:46:50 +0100 schrieb WM:
> 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).
ω, corresponding to „all”, is not natural.

>>>>> 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.
There is no FISON for ω (duh).

>>> 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.
Wrong. Finite sets of FISONs do not result in N.

-- 
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.