Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: WM Newsgroups: sci.math Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers Date: Sat, 30 Nov 2024 20:07:52 +0100 Organization: A noiseless patient Spider Lines: 17 Message-ID: References: <3fe6ef31f562e0ddf598de46cf864986ca909687@i2pn2.org> <9cb8aec671200bb6d71582fd607b876b7ec4c83a@i2pn2.org> <40292abc147fee5a7bdd264b69d34ddf2061e59d@i2pn2.org> <0bc3cdc8c096bba16decd94ad2af85d35da9b7b4@i2pn2.org> <9896cb31-806b-40a2-a03e-dc4aea744d04@att.net> <298a18e0-a0c6-4db2-901d-da255ecace0b@tha.de> <0b2e9a84-f5b3-4f02-8f78-7781da9175af@att.net> <47ccedfd-7c29-4c1a-a411-bbb0c27726e8@att.net> <890acbe4-3d0d-476f-be76-07fd33903746@att.net> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Sat, 30 Nov 2024 20:07:52 +0100 (CET) Injection-Info: dont-email.me; posting-host="ebfce87fb265da80d3fa3af64923c092"; logging-data="1945937"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/1LMBFkBSK0fc82yH3ctWH70m8lVTxZas=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:1rTNeJy20rhE85ZL6XZi7s/Bs1M= Content-Language: en-US In-Reply-To: <890acbe4-3d0d-476f-be76-07fd33903746@att.net> Bytes: 2439 On 30.11.2024 18:32, Jim Burns wrote: > Apparently, what you (WM) call "the intersection" > is each of infinitely.many intersections, and their limit. > Our sets do not change. But there is a sequence of endsegments E(1), E(2), E(3), ... and a sequence of their intersections E(1), E(1)∩E(2), E(1)∩E(2)∩E(3), ... . Both are identical - from the first endsegment on until every existing endsegment. Regards, WM