Path: ...!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: Tue, 25 Feb 2025 10:02:47 +0100 Organization: A noiseless patient Spider Lines: 21 Message-ID: References: <5220af0cb7d579f20d58809659d8dcb8d7ba046c@i2pn2.org> <685c1274-e22f-409d-b39c-c3a5430c2f57@att.net> <69f56ce0-08a2-4614-b102-e333175c643d@att.net> <9a88665f-211f-4260-b585-97c72c7b6d1b@att.net> <8bed122d8b355eff96158e6f5cb76cffcc42925c@i2pn2.org> <7a26856916099747e76314a2b4c79693e14426fd@i2pn2.org> <98baf83e-820e-4e1b-be2c-e5ea4802683d@att.net> <0876c2b9-2144-44c1-a26b-20176f5e2127@att.net> <067f772a-4f4c-4c27-8042-3f605f814876@att.net> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Tue, 25 Feb 2025 10:02:53 +0100 (CET) Injection-Info: dont-email.me; posting-host="356e11fa35ac2c14a6072e21beb6560b"; logging-data="1968813"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/m/hsK3b45ItNv42Aw3FpurQtmswI4omw=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:SwgI0jp4gFTmH1CoZhuOPGeRacU= Content-Language: en-US In-Reply-To: Bytes: 2636 On 24.02.2025 19:01, joes wrote: > Am Mon, 24 Feb 2025 15:59:18 +0100 schrieb WM: >> These axioms can be applied to show that all FISONs can be removed. > Nope. Any number of them can be removed. Indeed, removing all > changes the union, as you have admitted. There are not more than any number. >> Only all FISONs = natural numbers are the matter of my proof. According >> to Zermelo they make up the set ℕ. > The set N is not a natural number Of course. Nobody said so. > that the proof concerns. But Zermelo claims to produce the set ℕ. Is he wrong? Hint: In fact he produces ℕ_def. Regards, WM