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 Date: Tue, 19 Nov 2024 12:11:02 -0000 (UTC) Organization: i2pn2 (i2pn.org) Message-ID: References: <97304048-24f5-4625-82a7-d17427f2f6e3@att.net> <65febd06-662b-4fa4-9aa8-f7353a79a110@att.net> <157a949d-6c19-4693-8cee-9e067268ae45@att.net> <8165b44b-1ba5-429d-8317-0b043b214b53@att.net> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Injection-Date: Tue, 19 Nov 2024 12:11:02 -0000 (UTC) Injection-Info: i2pn2.org; logging-data="3184812"; 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: 2572 Lines: 17 Am Mon, 18 Nov 2024 19:20:24 +0100 schrieb WM: > On 18.11.2024 18:15, FromTheRafters wrote: >> WM brought next idea : > >>>> |ℕ| - |ℕ| = 0 because if you subtract one element from ℕ then you >>>> have no longer ℕ and therefore no longer |ℕ| describing it. > If you remove one element from ℕ, then you have still ℵo but no longer > all elements of ℕ. Yes, you have a subset of the same cardinality. > If |ℕ| describes the number of elements, then it has > changed to |ℕ| - 1. |N| - 1 = Aleph_0 - 1 = Aleph_0 -- 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.