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Failed to connect to MySQL: (1203) User howardkn already has more than 'max_user_connections' active connectionsPath: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail From: WM Newsgroups: sci.math Subject: Re: The set of necessary FISONs Date: Fri, 31 Jan 2025 11:21:58 +0100 Organization: A noiseless patient Spider Lines: 17 Message-ID: References: <27377646-137a-4f8f-a7bb-a75707b2da96@att.net> <965ee9868f28953d437113d0d38f069815499a3f@i2pn2.org> <77fb6230f3ef78f7524b70785c4772313e238258@i2pn2.org> <814297ada299a65bb9f427ddec5646afcc94be9f@i2pn2.org> <95ac176b19f1c24772a2ee73b3a12fe494da1241@i2pn2.org> <993b552f-7ab8-4a0b-a308-4748f20efb95@tha.de> <9e3c198cdfa1b264a1e30723ff18538f02e59af0@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Fri, 31 Jan 2025 11:21:58 +0100 (CET) Injection-Info: dont-email.me; posting-host="e88c9309437777936f7e1b85394b096b"; logging-data="3639824"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1+VkzmFMTT3QwzT3RE17mMbJ8TL4q4AoUM=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:kd2ZLz/tbq+qKmwf55q8KiykZ9g= In-Reply-To: Content-Language: en-US Bytes: 2548 On 31.01.2025 02:02, Richard Damon wrote: > On 1/30/25 2:28 PM, WM wrote: >> But a set that has union ℕ is a set. > > But since the "Set of Necessary FISONs" isn't actually a "Set" take the set O of v. Neumann ordinals A(n) that you claim satisfies U(A(n)) = ℕ. From this set O every finite subset can be subtracted without changing the result. Therefore, by induction, no finite A(n) remains. Therefore the set O has no first ordinal. Therefore it is not a set of ordinals. Therefore your claim is wrong. Regards, WM