Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail
From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary)
Date: Wed, 8 Jan 2025 15:31:13 +0100
Organization: A noiseless patient Spider
Lines: 17
Message-ID: <vlm27g$2qk9u$1@dont-email.me>
References: <vg7cp8$9jka$1@dont-email.me>
 <c03cf79d-0572-4b19-ad92-a0d12df53db9@att.net> <vkp0fv$b7ki$2@dont-email.me>
 <b125beff-cb76-4e5a-b8b8-e4c57ff468e9@att.net> <vkr8j0$t59a$1@dont-email.me>
 <98519289-0542-40ce-886e-b50b401ef8cf@att.net> <vksicn$16oaq$7@dont-email.me>
 <8e95dfce-05e7-4d31-b8f0-43bede36dc9b@att.net> <vl1ckt$2b4hr$1@dont-email.me>
 <53d93728-3442-4198-be92-5c9abe8a0a72@att.net> <vl5tds$39tut$1@dont-email.me>
 <9c18a839-9ab4-4778-84f2-481c77444254@att.net> <vl87n4$3qnct$1@dont-email.me>
 <8ef20494f573dc131234363177017bf9d6b647ee@i2pn2.org>
 <vl95ks$3vk27$2@dont-email.me> <vl9ldf$3796$1@dont-email.me>
 <vlaskd$cr0l$2@dont-email.me> <vlc68u$k8so$1@dont-email.me>
 <vldpj7$vlah$7@dont-email.me>
 <a8b010b748782966268688a38b58fe1a9b4cc087@i2pn2.org>
 <vlei6e$14nve$1@dont-email.me> <66868399-5c4b-4816-9a0c-369aaa824553@att.net>
 <vlir7p$24c51$1@dont-email.me> <412770ca-7386-403f-b7c2-61f671d8a667@att.net>
 <vllg47$2n0uj$3@dont-email.me> <b51a409b-8bf3-4cdb-9093-c6ed7c16eb15@att.net>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Wed, 08 Jan 2025 15:31:12 +0100 (CET)
Injection-Info: dont-email.me; posting-host="2032d15ede48f4ea5630c2af03a6b708";
	logging-data="2969918"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX19KmM9uxhNFFnGlwROpNycJcVlLr/e/qM8="
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:wTBnUnTDlxJ/KzsbTnfWrGXhbcI=
Content-Language: en-US
In-Reply-To: <b51a409b-8bf3-4cdb-9093-c6ed7c16eb15@att.net>
Bytes: 2673

On 08.01.2025 14:31, Jim Burns wrote:

> ⦃k: k < ω ≤ k+1⦄ = ⦃⦄
> ω-1 does not exist.
> 
Let us accept this result.

Then the sequence of endsegments loses every natnumber but not a last 
one. Then the empty intersection of infinite but inclusion monotonic 
endsegments is violating basic logic. (Losing all numbers but keeping 
infinitely many can only be possible if new numbers are acquired.) Then 
the only possible way to satisfy logic is the non-existence of ω and of 
endsegments as complete sets.

It is useless to prove your claim as long as you cannot solve this problem.

Regards, WM