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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.quux.org!news.nk.ca!rocksolid2!i2pn2.org!.POSTED!not-for-mail From: Richard Damon Newsgroups: comp.theory Subject: Re: Cantor Diagonal Proof Date: Thu, 10 Apr 2025 21:27:21 -0400 Organization: i2pn2 (i2pn.org) Message-ID: <6ce86dfd0bce01ed28b84f47d243cc1bc5365d75@i2pn2.org> References: <875xjfd5rs.fsf@nosuchdomain.example.com> <87tt6zblzl.fsf@nosuchdomain.example.com> <0920ac6e196c1cebeff36d8b9431ee12a7b3d527@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Fri, 11 Apr 2025 01:27:22 -0000 (UTC) Injection-Info: i2pn2.org; logging-data="4021561"; mail-complaints-to="usenet@i2pn2.org"; posting-account="diqKR1lalukngNWEqoq9/uFtbkm5U+w3w6FQ0yesrXg"; User-Agent: Mozilla Thunderbird X-Spam-Checker-Version: SpamAssassin 4.0.0 Content-Language: en-US In-Reply-To: Bytes: 3113 Lines: 27 On 4/10/25 8:29 PM, Lawrence D'Oliveiro wrote: > On Thu, 10 Apr 2025 10:37:49 +0300, Mikko wrote: > >> On 2025-04-10 00:50:10 +0000, Lawrence D'Oliveiro said: >> >>> On Mon, 7 Apr 2025 20:48:27 -0400, Richard Damon wrote: >>> >>>> The paper clearly talks about the process continuing indefinitely. >>> >>> Note the key point about any computation of a computable number is that >>> the answer *converges* to the exact result in the limit. As you compute >>> more and more digits, the discrepancy between your approximation and >>> the correct answer can be made as close to zero as you like, just as >>> long as you don’t ask for it to be zero. >>> >>> The Cantor construction does not converge. >> >> If it is a computable number it does converge. > > That’s a key point of my proof: if it converges, then the number is > already in the list. The only way it can come up with a number not in the > list is by never converging. it doesn't need to not converge, it just has to be different from every other number on the list, since he was just showing uncountable. Since it is different from the list of every contable number, it must be part of a larger set, and uncntable infinity.