Warning: mysqli::__construct(): (HY000/1203): User howardkn already has more than 'max_user_connections' active connections in D:\Inetpub\vhosts\howardknight.net\al.howardknight.net\includes\artfuncs.php on line 21
Failed to connect to MySQL: (1203) User howardkn already has more than 'max_user_connections' active connectionsPath: ...!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: Sat, 7 Dec 2024 17:33:12 -0800 Organization: A noiseless patient Spider Lines: 18 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: Sun, 08 Dec 2024 02:33:12 +0100 (CET) Injection-Info: dont-email.me; posting-host="021479c43f8aee38ea8f1e7f736414c6"; logging-data="3597760"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/Yf+7RzctFw5H2uQbtqOcluAMJ0hyGdcU=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:YoAq7VDghQurxpepLi0jDJXPO5o= In-Reply-To: Content-Language: en-US Bytes: 2752 On 12/7/2024 1:38 PM, Moebius wrote: > Am 07.12.2024 um 22:20 schrieb Chris M. Thomasson: > >> Have you ever implemented a Cantor Pairing function that can go back >> and forth wrt the original number to unique pair and back to the >> original number? They are pretty fun to play around with. > > Actually, I've implemented a complete library for (finite) "sets" in C. :-) > > Does that count? > > Well, that's fine. Wrt this subject its all about a Cantor pairing. Take any natural, (yes zero works as well) and be able to map it into a 100% unique pairing. Then say okay, we have this unique pair. Now, we are able to take said unique pair and map it right back to the natural that created it to begin with.