Path: ...!weretis.net!feeder9.news.weretis.net!news.quux.org!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: "Chris M. Thomasson" Newsgroups: sci.math Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary) Date: Thu, 5 Dec 2024 16:30:57 -0800 Organization: A noiseless patient Spider Lines: 10 Message-ID: References: <87frn50zjp.fsf@bsb.me.uk> <87y10vzo35.fsf@bsb.me.uk> <87ser3zgez.fsf@bsb.me.uk> <52bcdc5dc54bbfb48a16c985885e5d527e483ceb@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 7bit Injection-Date: Fri, 06 Dec 2024 01:30:57 +0100 (CET) Injection-Info: dont-email.me; posting-host="60cc1b43a0c5f0f5562bde95bed4a8a0"; logging-data="2032336"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/Hz/aLUrjCqKVKzH2n0xpHzgA7PK6G/bs=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:3Z44YLTzDa5hkAa983AscM0ontU= Content-Language: en-US In-Reply-To: Bytes: 2301 On 12/5/2024 8:08 AM, WM wrote: > On 05.12.2024 13:26, Richard Damon wrote: > >> Which ones can not be "taken" or "given". > > Those with less than infinitely many successors. Cantor claims that all > numbers are in his bijections. No successors remaining. Do you even know how to take any natural number, create a unique pair and then get back to the original number from said pair?