Path: news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail From: WM Newsgroups: sci.math Subject: Re: The set of necessary FISONs Date: Mon, 27 Jan 2025 15:33:01 +0100 Organization: A noiseless patient Spider Lines: 15 Message-ID: References: <903de8e1-3538-4cfe-9f7a-6509eda47ab6@att.net> <3844edd7-0750-4418-bff6-2759817446b3@att.net> <27377646-137a-4f8f-a7bb-a75707b2da96@att.net> <965ee9868f28953d437113d0d38f069815499a3f@i2pn2.org> <77fb6230f3ef78f7524b70785c4772313e238258@i2pn2.org> <814297ada299a65bb9f427ddec5646afcc94be9f@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Mon, 27 Jan 2025 15:33:01 +0100 (CET) Injection-Info: dont-email.me; posting-host="1fc5ef77a148ddf2f7d4705f9be5faad"; logging-data="991028"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX18DV1N7EH0UlvijMHGd7J6HZIUKkctuNl8=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:tIU+d5tKvqiMznEPT4sygtxpT7E= In-Reply-To: <814297ada299a65bb9f427ddec5646afcc94be9f@i2pn2.org> Content-Language: en-US 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. But no FISON is necessary or sufficient. Regards, WM