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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, 21 Feb 2025 10:32:07 +0100 Organization: A noiseless patient Spider Lines: 40 Message-ID: References: <5aefc0d0b454a230e721a8cdb8400cb25ea9a8c1@i2pn2.org> <340761ab1ceb68741d949331a0c64a3d6d5fa237@i2pn2.org> <865ffa4c4c1091981c5b3b93ddf3dba690cd5ad2@i2pn2.org> <559d228c01ea290aec13e735ec85036862578165@i2pn2.org> <5220af0cb7d579f20d58809659d8dcb8d7ba046c@i2pn2.org> <325c90249ce4a619cc8a7f7b19b4884d12bc58aa@i2pn2.org> <75ad3257-06f3-4f71-99bf-82227ccadde2@att.net> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Fri, 21 Feb 2025 10:32:06 +0100 (CET) Injection-Info: dont-email.me; posting-host="b402164b407b86488ec8b39155ff4361"; logging-data="3489748"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/aFclruz8ncBT66ghfEHd2OsKCJUBoVfE=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:uOZQ/3l3I3pdUTf0oRQUOaIES/8= Content-Language: en-US In-Reply-To: Bytes: 2890 On 20.02.2025 21:24, Jim Burns wrote: > On 2/20/2025 2:27 PM, WM wrote: > Are you denying that {i:j+1≤i≤k+1} exists? > > Are you denying that {i:j+1≤i≤k+1} is > larger than {i:i≤k} ? Induction covers all infinitely many elements. Induction proves that no FISON is changing the assumed union ℕ. > >>>> That contradicts the assumption. >>> >>> What is the assumption? >> >> The assumption is the existence of S. >> >>> What is the contradiction? >> >> The contradiction is that >> induction proves every FISON useless > > Each FISON being uselessᵂᴹ (not.last) Useless is every FISON smaller than ℕ whether or not being last. (Note there is no last FISON.) > is > a consequence of ⋃S > being the only.inductive.subset of ⋃S > And vice versa. Whatever > > What are the TWO statements which > contradict each other? UF = ℕ and UF = ℕ ==> Ø = ℕ. Regards, WM