Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail
From: FromTheRafters <FTR@nomail.afraid.org>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)
Date: Thu, 12 Dec 2024 14:06:07 -0500
Organization: Peripheral Visions
Lines: 23
Message-ID: <vjfc75$2t3e7$1@dont-email.me>
References: <vg7cp8$9jka$1@dont-email.me>   <3af23566-0dfc-4001-b19b-96e5d4110fee@tha.de> <ae606e53-0ded-4101-9685-fa33c9a35cb9@att.net> <viuc2a$27gm1$1@dont-email.me> <8a53c5d4-4afd-4f25-b1da-30d57e7fe91c@att.net> <vj1acu$31atn$3@dont-email.me> <ec451cd6-16ba-463d-8658-8588093e1696@att.net> <vj2f61$3b1no$1@dont-email.me> <10ebeeea-6712-4544-870b-92803ee1e398@att.net> <vj3tl0$3nktg$2@dont-email.me> <1f1a4089-dfeb-45f8-9c48-a36f6a4688fb@att.net> <vj6bqo$b6bt$1@dont-email.me> <b09445be167b757878741be04c87cf76d24d9786@i2pn2.org> <vj6psc$dp01$1@dont-email.me> <84818a4f5d3795b746b017ad0861a3d818c5b053@i2pn2.org> <vj8vd0$stav$1@dont-email.me> <5805ad50ebff3400d1370d8c99790cbc727a340a@i2pn2.org> <e86171d3-e5c1-4725-952d-d4da0f4ded07@tha.de> <1ac93432f1ba567e0f15308b8964bee86b92c706@i2pn2.org> <vjc7q2$1ir2f$2@dont-email.me> <4e7901e16785581d0d02a2d6474d7d2615c5fac9@i2pn2.org> <vje9dp$229c8$1@dont-email.me> <vjehh0$23up4$1@dont-email.me> <vjerk8$25pc3$1@dont-email.me>
Reply-To: erratic.howard@gmail.com
MIME-Version: 1.0
Content-Type: text/plain; charset="iso-8859-15"; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Thu, 12 Dec 2024 20:06:14 +0100 (CET)
Injection-Info: dont-email.me; posting-host="04a388e9879200df965ef9c916d328e3";
	logging-data="3050951"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX1/Z6FxkcItzb7GpY8sLbyQdFkWFPsQJQRk="
Cancel-Lock: sha1:9AAZ376EAI8/Y+P8lQgt7O1hDUM=
X-Newsreader: MesNews/1.08.06.00-gb
X-ICQ: 1701145376
Bytes: 2603

WM was thinking very hard :
> On 12.12.2024 12:30, FromTheRafters wrote:
>> WM wrote :
>
>>>
>>> Most endsegments are infinite.
>> 
>> Many endsegments are infinite too.
>
> Most endsegments are infinite.

Some endsegments are infinite.

> But if Cantor can apply all natural numbers as indices for his bijections, 
> then all must leave the sequence of endsegments.  Then the sequence (E(k)) 
> must end up empty.

Impossible, since k and k+1 etcetera are natural numbers.

> And there must be a continuous staircase from E(k) to the empty set.

A limit set or element does not have to be completely within a set or 
interval.