Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: WM Newsgroups: sci.logic Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary) Date: Tue, 10 Dec 2024 18:01:04 +0100 Organization: A noiseless patient Spider Lines: 13 Message-ID: References: <0b1bb1a1-40e3-464f-9e3d-a5ac22dfdc6f@tha.de> <95183b4d9c2e32651963bac79965313ad2bfe7e8@i2pn2.org> <33512b63716ac263c16b7d64cd1d77578c8aea9d@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 7bit Injection-Date: Tue, 10 Dec 2024 18:01:06 +0100 (CET) Injection-Info: dont-email.me; posting-host="76161c015d6b8237a412351767b0136f"; logging-data="1091705"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX19gyV2TRY/rdUxyjWJ0WMo5vwtHA7gLBF8=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:/mC3tdGBKJfDfXVy+0RS1cvpBME= Content-Language: en-US In-Reply-To: <33512b63716ac263c16b7d64cd1d77578c8aea9d@i2pn2.org> Bytes: 2464 On 10.12.2024 13:19, Richard Damon wrote: > > The pairing is between TWO sets, not the members of a set with itself. The pairing is between the elements. Otherwise you could pair R and Q by simply claiming it. "The infinite sequence thus defined has the peculiar property to contain the positive rational numbers completely, and each of them only once at a determined place." [Cantor] Note the numbers, not the set. Regards, WM