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From: FromTheRafters <FTR@nomail.afraid.org>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)
Date: Mon, 20 Jan 2025 09:31:53 -0500
Organization: Peripheral Visions
Lines: 11
Message-ID: <vmlmos$36pcp$1@dont-email.me>
References: <vg7cp8$9jka$1@dont-email.me>   <vlrej9$2m5k$1@dont-email.me> <d6ed4797-65e8-4004-853c-f07a37af0c11@att.net> <vls4j6$7v2k$3@dont-email.me> <494bfd3b-3c70-4d8d-9c70-ce917c15fc22@att.net> <vm0okb$16cq0$2@dont-email.me> <bff18686-503a-4b7b-9406-b47796f68b47@att.net> <vm15pj$18v7t$1@dont-email.me> <72142d82-0d71-460a-a1be-cadadf78c048@att.net> <vm3hrs$1s9ld$2@dont-email.me> <812e64b1-c85c-48ac-a58c-e8955bc02f8c@att.net> <vm59g4$2b5ib$1@dont-email.me> <22b74adc-bf38-4aa4-a44f-622f0a2a5c41@att.net> <vm8u36$31v8s$5@dont-email.me> <77a1069f5c5b8f95927ed9a33ecc6374c9d0a2dd@i2pn2.org> <vmb821$3i6nm$1@dont-email.me> <da8e83072697acf06f9ca2b2946d7b9ccfcbcaac@i2pn2.org> <20e517f6-d709-46fd-83f8-04c6b4fe9f59@tha.de> <4679319ea238a03fb042ae0c4de078c1a310c8a5@i2pn2.org> <vmejlt$845r$1@dont-email.me> <21586c471d7da511d9a2bc75fb13ee29f30e4e66@i2pn2.org> <vmil8m$252qj$2@dont-email.me> <f93aa4ee481c73918867d4cfc78229461805770a@i2pn2.org> <vmlghd$34j33$2@dont-email.me>
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It happens that WM formulated :
> On 19.01.2025 16:10, joes wrote:
>> Am Sun, 19 Jan 2025 11:47:50 +0100 schrieb WM:
>
>>> They contain only natnumbers which have ℵ₀ successors.
>> There are no naturals with a finite number of successors, otherwise
>> you could count backwards from the end.
>
> That is possible: ω-1, ω-2, ω-3, ...

Wrong, omega has no immediate predecessor.