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Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail 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> Reply-To: erratic.howard@gmail.com MIME-Version: 1.0 Content-Type: text/plain; charset="utf-8"; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Sun, 02 Mar 2025 14:41:19 +0100 (CET) Injection-Info: dont-email.me; posting-host="074ab56572eb897ab82f623e62f21588"; logging-data="853496"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/Td5C8MIW4wj057aB6g2bH0mUiC5x6buU=" Cancel-Lock: sha1:GnJLW5hxH4QuE7w0Tqw7gunmcA0= X-Newsreader: MesNews/1.08.06.00-gb X-ICQ: 1701145376 Bytes: 3093 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. AI Chatbot https://poe.com/chat/370x9xpc7krhbconr8j Assistant Poe 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}.