Path: ...!news.misty.com!weretis.net!feeder9.news.weretis.net!news.nk.ca!rocksolid2!i2pn2.org!.POSTED!not-for-mail From: joes Newsgroups: sci.math Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary) Date: Sat, 28 Dec 2024 19:35:52 -0000 (UTC) Organization: i2pn2 (i2pn.org) Message-ID: <8a5ea464a97000a9e3e8cad62bd9d2a0f5aa5742@i2pn2.org> References: <33512b63716ac263c16b7d64cd1d77578c8aea9d@i2pn2.org> <069069bf23698c157ddfd9b62b9b2f632b484c40@i2pn2.org> <2d3620a6e2a8a57d9db7a33c9d476fe03cac455b@i2pn2.org> <75921cc1f17cdb691969a99e666f237cd09c0b09@i2pn2.org> <25729298b142c60d5b245231984119d42d4ac089@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Injection-Date: Sat, 28 Dec 2024 19:35:52 -0000 (UTC) Injection-Info: i2pn2.org; logging-data="832983"; 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: 2650 Lines: 18 Am Sat, 28 Dec 2024 14:58:50 +0100 schrieb WM: > On 28.12.2024 06:23, Moebius wrote: >>>> On 12/17/24 4:51 PM, WM wrote: >> >>>>> all FISONs contain/are all n. > All FISONs contain all *definable* n. Which, in standard mathematics, is all inf. many of them >> Hint: For each and every n e IN there is a FISON such that n is in it. >> BUT there's no FISON such that each and every n e IN is in it. > Every FISON contains less than half of all natural numbers. Almost none, actually, N being infinite and all. > Therefore > the union of all of them contains less than half of all natural numbers. Worng. -- 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.