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Failed to connect to MySQL: (1203) User howardkn already has more than 'max_user_connections' active connectionsPath: 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, 14 Feb 2025 17:40:34 +0100 Organization: A noiseless patient Spider Lines: 24 Message-ID: References: <11e634bd-c1d3-4d72-9e18-be6ca22b4742@att.net> <999fb07e-7bef-4423-afeb-a08922613c65@att.net> <0d24c3fd-cd63-4e21-9dd4-ab1360560b09@att.net> <79920977-902d-4f59-a11c-497383221c82@att.net> <468b9c37-ba93-485c-8685-4b320e168251@att.net> <68bab5c2-50d3-43fc-be0d-51e01c5952bb@att.net> <862117d5-9944-4eaa-9bbf-040e376c27e1@att.net> <61fda474-8104-4e37-a1cc-d9fec975bdc5@att.net> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Fri, 14 Feb 2025 17:40:35 +0100 (CET) Injection-Info: dont-email.me; posting-host="bb2d630d22d9ab3d5a86c2cc7ceb66b9"; logging-data="3733580"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1++E41+vvDWkv80lec5jhkzs6IwxTQF2Ag=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:V93+mtL8fuxaE2fg7UqYHnJc5AM= In-Reply-To: <61fda474-8104-4e37-a1cc-d9fec975bdc5@att.net> Content-Language: en-US On 14.02.2025 16:42, Jim Burns wrote: > On 2/14/2025 7:52 AM, WM wrote: >> Induction creates infinite sets. > > Zermelo set theory [I...VII] describes > a domain of discourse with > Z an inductiveᶻ set Where all elements are covered by induction. >> If i contruct x(1) and from x(n) follows x(n+1) >> then the set of all x(n) is infinite. > > then the set of all x(n) is > an inductive subset of the minimal.inductive set. And no element is outside. > There is no set of all FISON.numbers in ST+F. But it is the result of the proof. There is not the least doubt that no FISON remains for constructing ℕ. Regards, WM