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From: FromTheRafters <FTR@nomail.afraid.org>
Newsgroups: sci.math
Subject: Re: The set of necessary FISONs
Date: Sun, 02 Mar 2025 08:41:16 -0500
Organization: Peripheral Visions
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WM brought next idea :
> On 01.03.2025 19:38, FromTheRafters wrote:
>> WM presented the following explanation :
>
>>> Processes using defined individuals like FISONs cannot surpass a finite 
>>> set. FISONs are finite. Their number will never be greater than finite.
>>> {1}
>>> {2, 1}
>>> {3, 2, 1}
>>> ...
>> 
>> Those are still not FISONs.
>
> They are. The order in curly brackets does not matter.

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The term "FISON" stands for "finite initial segment of natural 
numbers." A FISON is typically defined as a finite set of the form 
{0,1,2,…,n} for some non-negative integer n.

The set {4,3,2,1} does not meet this definition for a couple of 
reasons:

    Order: A FISON must include all natural numbers starting from 0 up 
to n in ascending order. The set {4,3,2,1} is not in ascending order 
and does not include 0.

    Completeness: A FISON must include all natural numbers less than or 
equal to its maximum element. In this case, the maximum element is 4, 
but the set is missing 0.

Therefore, {4,3,2,1} is not a FISON. A valid FISON that includes up to 
4 would be {0,1,2,3,4}.