Path: ...!news.misty.com!weretis.net!feeder9.news.weretis.net!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, 16 Dec 2024 11:49:00 -0000 (UTC) Organization: i2pn2 (i2pn.org) Message-ID: <667b80630f56e3de0883e8e664cc6c6338315792@i2pn2.org> References: <10fbe4d3-a1d1-4740-8d23-8cd96f3b9bfc@att.net> <696c5a55-3cb6-4fa7-bd11-9b8f8eeeaef7@att.net> <3f902f42-e435-4a44-a179-687ad2a33f16@att.net> <4f0bc5b5-aba7-4c19-91f7-d4f9788591a0@att.net> <6c74c2e9-17d7-4eb4-afcd-c058309b6c8a@tha.de> <4327ba4a-e810-4565-83e8-b9572018ac35@att.net> <409e6573b219f41f359193f128cd002cc74a7243@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Injection-Date: Mon, 16 Dec 2024 11:49:00 -0000 (UTC) Injection-Info: i2pn2.org; logging-data="3093819"; 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: 2441 Lines: 13 Am Mon, 16 Dec 2024 09:50:14 +0100 schrieb WM: > On 15.12.2024 22:13, Richard Damon wrote: >> On 12/15/24 1:57 PM, WM wrote: > >>> Dark numbers are required to empty ℕ by |ℕ \ {1, 2, 3, ...}| = 0. All >>> definable numbers fail: ∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo. > >> And why do you need to do that? > In order to show the existence of dark numbers. It just shows the infinity of n. No natural is as large as N. -- 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.