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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
Lines: 39
Message-ID: <vq1n5u$q1fo$1@dont-email.me>
References: <vmo1bs$1rnl$1@dont-email.me>   <vpetjf$eusv$3@dont-email.me> <98baf83e-820e-4e1b-be2c-e5ea4802683d@att.net> <vpfc74$hq5c$2@dont-email.me> <0876c2b9-2144-44c1-a26b-20176f5e2127@att.net> <vpft4t$kdg0$4@dont-email.me> <067f772a-4f4c-4c27-8042-3f605f814876@att.net> <vpi1g6$14ivq$7@dont-email.me> <c658f0ca1b716eb4d123389266476f35abcc367a@i2pn2.org> <vpk0vs$1s2ld$1@dont-email.me> <fce30f5e64c402934fa457a67f1d9559a89ec74d@i2pn2.org> <vpk42o$1siqa$2@dont-email.me> <c4e441d0339bbcf17714a6c8c517304df7ce802c@i2pn2.org> <vpkjf1$2025c$3@dont-email.me> <d05673e8740751d8cbf6bce1f5390e3c5479b7e4@i2pn2.org> <vpmvn3$2i1ev$2@dont-email.me> <ca2abaa2984854d6c165f77f9daa8ebe77a87e00@i2pn2.org> <vppg83$3280b$2@dont-email.me> <4bce9826fcd4c68b4785aabc83de9394eae61402@i2pn2.org> <vpsp51$3mn6v$4@dont-email.me> <2a62cfa0db610ef9bb26903f8e9417e96e1bfa57@i2pn2.org> <vpv5oq$8kkq$1@dont-email.me> <vpvk7q$bf6k$1@dont-email.me> <vq16jp$n5t1$1@dont-email.me>
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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}.