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: Fri, 29 Nov 2024 16:50:20 -0500
Organization: Peripheral Visions
Lines: 24
Message-ID: <vidcv3$18pdu$1@dont-email.me>
References: <vg7cp8$9jka$1@dont-email.me>   <vhvbs4$28n6o$2@dont-email.me> <09f8a86f-3f75-4af8-a190-0def76c1ab82@att.net> <vhvviq$2bjrd$1@dont-email.me> <68dc9b71-cf5d-4614-94e2-8a616e722a63@att.net> <vi03un$2cv9g$1@dont-email.me> <67d9867b-2614-4475-975c-938bafca5c00@att.net> <vi1vep$2pjuo$1@dont-email.me> <a4ab640d-e482-42b0-bfb8-f3690b935ce1@att.net> <vi41rg$3cj8q$1@dont-email.me> <d124760c-9ff9-479f-b687-482c108adf68@att.net> <vi56or$3j04f$1@dont-email.me> <4a810760-86a1-44bb-a191-28f70e0b361b@att.net> <vi6uc3$3v0dn$4@dont-email.me> <b2d7ee1f-33ab-44b6-ac90-558ac2f768a7@att.net> <vi7tnf$4oqa$1@dont-email.me> <23311c1a-1487-4ee4-a822-cd965bd024a0@att.net> <e9eb6455-ed0e-43f6-9a53-61aa3757d22d@tha.de> <71758f338eb239b7419418f49dfd8177c59d778b@i2pn2.org> <via83s$jk72$2@dont-email.me> <viag8h$lvep$1@dont-email.me> <viaj9q$l91n$1@dont-email.me> <vibvfo$10t7o$1@dont-email.me> <vic6m9$11mrq$4@dont-email.me> <vicbp2$1316h$1@dont-email.me> <vid4ts$1777k$2@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: Fri, 29 Nov 2024 22:50:28 +0100 (CET)
Injection-Info: dont-email.me; posting-host="aa8b95b3872ada84f63765f0ac015959";
	logging-data="1336766"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX19MZ1II5u7JwUWXmaM2dB86y1O5r/J6i7g="
Cancel-Lock: sha1:PXjyf1AVbiE3SK8DwU5gtTlh8PU=
X-Newsreader: MesNews/1.08.06.00-gb
X-ICQ: 1701145376
Bytes: 3077

WM wrote on 11/29/2024 :
> On 29.11.2024 13:23, FromTheRafters wrote:
>> WM was thinking very hard :
>>> On 29.11.2024 09:54, FromTheRafters wrote:
>>>> WM expressed precisely :
>>>
>>>>> But as long as infinitely many natnumbers have not left the endsegments, 
>>>>> they stay inside all of them. And many are the same for all endsegments. 
>>>>> Therefore the intersection of infinite endsegments is infinite.
>>>>
>>>> Natural numbers don't "leave", sets don't change.
>>>
>>> Call it as you like. Fact is that the function of endsegments is losing 
>>> elements. The limit is the empty endsegment.
>> 
>> Your sequence of endsegments (which are each countably infinte) is indeed 
>> losing an element of N with each iteration. Losing an element is not the 
>> same as reducing an infinite set's size though.
>
> The size of the intersection remains infinite as long as all endsegments 
> remain infinite (= as long as only infinite endsegments are considered).

Don't be so stupid. Endsegments are defined as infinite, all of them 
and each and every one of them. The intersection is empty.