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From: FromTheRafters <FTR@nomail.afraid.org>
Newsgroups: sci.math
Subject: Re: The set of necessary FISONs
Date: Sat, 01 Feb 2025 10:03:38 -0500
Organization: Peripheral Visions
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WM submitted this idea :
> 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.

They represent the finite ordinals. The set of all FISONs represents 
the first transfinite ordinal. FISONs also represent finite cardinals.