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Failed to connect to MySQL: (1203) User howardkn already has more than 'max_user_connections' active connectionsPath: ...!eternal-september.org!feeder3.eternal-september.org!i2pn.org!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: Mon, 2 Dec 2024 14:52:03 -0000 (UTC) Organization: i2pn2 (i2pn.org) Message-ID: <16f11466920516ccf0be2887aec3564e4f0cb8db@i2pn2.org> References: <4a810760-86a1-44bb-a191-28f70e0b361b@att.net> <23311c1a-1487-4ee4-a822-cd965bd024a0@att.net> <71758f338eb239b7419418f49dfd8177c59d778b@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Injection-Date: Mon, 2 Dec 2024 14:52:03 -0000 (UTC) Injection-Info: i2pn2.org; logging-data="907082"; 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: 2900 Lines: 26 Am Mon, 02 Dec 2024 15:28:30 +0100 schrieb WM: > On 02.12.2024 12:53, FromTheRafters wrote: > >>>> Endsegment E(n) = {n, n+1, n+2, ...} >> This is his definition of endsegment, which as almost anyone can see, >> has no last element, so yes it is infinite. He says 'infinite >> endsegment' as if there were a choice, only to add confusion. > Infinite endsegments contain an infinite set each They ARE infinite sets. > infinitely many elements of which are in the intersection. The intersection of all infinite segments? > An empty intersection cannot > come before an empty endsegment has been produced by losing one element > at every step. Which happens only in the limit. > E(1), E(2), E(3), ... > and E(1), E(1)∩E(2), E(1)∩E(2)∩E(3), ... > are identical for every n and in the limit because E(1)∩E(2)∩...∩E(n) = > E(n). What do you reckon the limit is? -- 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.