Path: ...!feeder3.eternal-september.org!news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail From: WM Newsgroups: sci.math Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary, effectively) Date: Sun, 29 Dec 2024 18:53:18 +0100 Organization: A noiseless patient Spider Lines: 19 Message-ID: References: <7356267c-491b-45c2-b86a-d40c45dfa40c@att.net> <4bf8a77e-4b2a-471f-9075-0b063098153f@att.net> <31180d7e-1c2b-4e2b-b8d6-e3e62f05da43@att.net> <45a632ed-26cc-4730-a8dd-1e504d6df549@att.net> <15f183ae29abb8c09c0915ee3c8355634636da31@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Sun, 29 Dec 2024 18:53:18 +0100 (CET) Injection-Info: dont-email.me; posting-host="2bdd8289678d0293abd2ca3e7b98ed0b"; logging-data="1172691"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX19FVMwbjUNY4CM1tqmHwSRySfIdCPyMgsk=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:85FZRuV3dFDl4L7tp9kQbAIvcX0= Content-Language: en-US In-Reply-To: Bytes: 2495 On 29.12.2024 13:34, Richard Damon wrote: > On 12/29/24 6:01 AM, WM wrote: >> >> All definable numbers (FISONs) stay below 1 %. Every union of "below 1 >> %" stays below 1 %. > > Since 0 is Less than 1, you are sort of correct, but that fact doesn't > prove your claim. > > The problem is that when you get to *ALL* I get to all FISONs below a certain threshold, namely a threshold between which and ω there exist ℵ₀ natnumbers. Regards, WM