Path: ...!weretis.net!feeder9.news.weretis.net!news.quux.org!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: Sun, 2 Feb 2025 12:34:55 +0100 Organization: A noiseless patient Spider Lines: 14 Message-ID: References: <4d349964-211f-42f1-936f-81c22ae54cb5@att.net> <6e0c8ab2-402a-43a5-a348-0c727eae6a2e@att.net> <87e2e677c7802c9c17df6063f340cb5857d5700b@i2pn2.org> <680d4249c9bf1504231a53732ac5096184261495@i2pn2.org> <5cc37d5ccc25d192843fcaf87e7418be0e9c5136@i2pn2.org> <080c854de10093669d87615694e51dd052ed2394@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Sun, 02 Feb 2025 12:34:56 +0100 (CET) Injection-Info: dont-email.me; posting-host="7889779fdd80798ffa0e9c506aa81a71"; logging-data="676672"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1+N0GiH34G8JMggNJI+NhEayEp6tOkP7RI=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:mVJiowbauQRcM3tT6G2/qiBYjLw= In-Reply-To: Content-Language: en-US Bytes: 2472 On 02.02.2025 01:33, Richard Damon wrote: > On 2/1/25 1:17 PM, WM wrote: >> The set of FISONs assumed to satisfy U(A(n)) = ℕ cannot be empty. But >> we can prove by induction that every FISON can be discarded without >> changing the union. That disproves the assumption. >> > And that is your problem, you make assumptions that are unwarented, I think you've got it! Yes, U(A(n)) is not ℕ. Regards, WM