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Path: 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: Mon, 27 Jan 2025 10:23:27 -0500 Organization: Peripheral Visions Lines: 15 Message-ID: <vn88di$10e3c$1@dont-email.me> References: <vmo1bs$1rnl$1@dont-email.me> <ee4e189d-56bc-4ed7-b7b7-cd71fc4d2349@att.net> <vmqh9k$urua$1@dont-email.me> <903de8e1-3538-4cfe-9f7a-6509eda47ab6@att.net> <vmsvfv$1hn5k$1@dont-email.me> <3844edd7-0750-4418-bff6-2759817446b3@att.net> <vmvn1h$25r19$1@dont-email.me> <27377646-137a-4f8f-a7bb-a75707b2da96@att.net> <vn2gcf$2ouuo$2@dont-email.me> <965ee9868f28953d437113d0d38f069815499a3f@i2pn2.org> <vn4sfi$3ijdb$2@dont-email.me> <e51fcde5622ccc6beab7882831e5f7033c04d150@i2pn2.org> <vn5gur$3qu1c$3@dont-email.me> <77fb6230f3ef78f7524b70785c4772313e238258@i2pn2.org> <vn7r2r$q7sl$2@dont-email.me> <814297ada299a65bb9f427ddec5646afcc94be9f@i2pn2.org> <vn85es$u7pk$2@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: Mon, 27 Jan 2025 16:23:31 +0100 (CET) Injection-Info: dont-email.me; posting-host="9e11361f58d829939c6bc970b036b306"; logging-data="1063020"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX19YjxgMdb1+m6GEpwSD72VQSsc+hylYvBg=" Cancel-Lock: sha1:hmzmubBtiDlGmSKJyrNzEL6WP8M= X-ICQ: 1701145376 X-Newsreader: MesNews/1.08.06.00-gb WM wrote : > On 27.01.2025 15:14, joes wrote: >> Am Mon, 27 Jan 2025 12:35:56 +0100 schrieb WM: >>> On 26.01.2025 23:31, Richard Damon wrote: >> >>>> you can't show that the first FISON isn't a member of the set of >>>> necessary FISONs without assuming the set of necessary FISONs exists. >>> >>> Logic? The set ℕ exists. And I can show that every FISON is neither >>> necessary nor sufficient to accomplish that aim. >> Obviously, but not for infinite sets of FISONs. > > Also an infinite set needs a first element. The real numbers are an infinite set, which one is first?