Path: ...!weretis.net!feeder9.news.weretis.net!news.quux.org!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) Date: Sun, 29 Dec 2024 18:56:23 +0100 Organization: A noiseless patient Spider Lines: 14 Message-ID: References: <069069bf23698c157ddfd9b62b9b2f632b484c40@i2pn2.org> <2d3620a6e2a8a57d9db7a33c9d476fe03cac455b@i2pn2.org> <75921cc1f17cdb691969a99e666f237cd09c0b09@i2pn2.org> <25729298b142c60d5b245231984119d42d4ac089@i2pn2.org> <8a5ea464a97000a9e3e8cad62bd9d2a0f5aa5742@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 18:56:23 +0100 (CET) Injection-Info: dont-email.me; posting-host="2bdd8289678d0293abd2ca3e7b98ed0b"; logging-data="1172691"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/jfnqD9fajSbzn354WSPmswaeiywzX41o=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:I10P7mgtfZC42ikozF/nrRDkDpM= In-Reply-To: Content-Language: en-US Bytes: 2520 On 29.12.2024 15:43, joes wrote: > Am Sun, 29 Dec 2024 12:05:26 +0100 schrieb WM: >> My theorem: If all definable numbers (FISONs) stay below a certain >> threshold, then every union of those FISONs stays below that threshold. > The infinite union doesn’t. > The union of all FISONs below a certain threshold, namely a threshold between which and ω there exist ℵ₀ natnumbers, remains below this very threshold. Regards, WM