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Path: ...!eternal-september.org!feeder3.eternal-september.org!i2pn.org!i2pn2.org!.POSTED!not-for-mail From: joes <noreply@example.org> Newsgroups: sci.math Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary) Date: Fri, 10 Jan 2025 08:52:39 -0000 (UTC) Organization: i2pn2 (i2pn.org) Message-ID: <3843025c38ccd3e0c669086eab08e88d09578d2e@i2pn2.org> References: <vg7cp8$9jka$1@dont-email.me> <vl1ckt$2b4hr$1@dont-email.me> <53d93728-3442-4198-be92-5c9abe8a0a72@att.net> <vl5tds$39tut$1@dont-email.me> <9c18a839-9ab4-4778-84f2-481c77444254@att.net> <vl87n4$3qnct$1@dont-email.me> <8ef20494f573dc131234363177017bf9d6b647ee@i2pn2.org> <vl95ks$3vk27$2@dont-email.me> <vl9ldf$3796$1@dont-email.me> <vlaskd$cr0l$2@dont-email.me> <vlc68u$k8so$1@dont-email.me> <vldpj7$vlah$7@dont-email.me> <a8b010b748782966268688a38b58fe1a9b4cc087@i2pn2.org> <vlei6e$14nve$1@dont-email.me> <66868399-5c4b-4816-9a0c-369aaa824553@att.net> <vlir7p$24c51$1@dont-email.me> <412770ca-7386-403f-b7c2-61f671d8a667@att.net> <vllg47$2n0uj$3@dont-email.me> <b51a409b-8bf3-4cdb-9093-c6ed7c16eb15@att.net> <vlm27g$2qk9u$1@dont-email.me> <56517e7b-7fa0-4ea8-88f4-bbd4c385e8d2@att.net> <vlp4ai$3fug2$1@dont-email.me> <84f157d6-b01d-436e-a99c-eb60bf250a22@att.net> <vlpb7k$3fug2$2@dont-email.me> <a9d88ef1-5bc4-4322-aa24-dc36421ba84e@att.net> <vlpjb4$3is52$2@dont-email.me> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Injection-Date: Fri, 10 Jan 2025 08:52:39 -0000 (UTC) Injection-Info: i2pn2.org; logging-data="2904003"; mail-complaints-to="usenet@i2pn2.org"; posting-account="nS1KMHaUuWOnF/ukOJzx6Ssd8y16q9UPs1GZ+I3D0CM"; User-Agent: Pan/0.145 (Duplicitous mercenary valetism; d7e168a git.gnome.org/pan2) X-Spam-Checker-Version: SpamAssassin 4.0.0 Bytes: 2406 Lines: 11 Am Thu, 09 Jan 2025 23:41:40 +0100 schrieb WM: > On 09.01.2025 23:05, Jim Burns wrote: >> On 1/9/2025 3:23 PM, WM wrote: > >> Thus, because ordinals are well.ordered, > an infinite set of endsegments requires all natural numbers as indices. > That means the content becomes/is empty if the set becomes/is infinite. There is no "infinitieth" index with an empty content. -- Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math: It is not guaranteed that n+1 exists for every n.