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Failed to connect to MySQL: (1203) User howardkn already has more than 'max_user_connections' active connectionsPath: ...!weretis.net!feeder8.news.weretis.net!pasdenom.info!from-devjntp Message-ID: JNTP-Route: news2.nemoweb.net JNTP-DataType: Article Subject: Re: Contradiction of bijections as a measure for infinite sets References: Newsgroups: sci.math JNTP-HashClient: JD1v9hUQw0hPI3xI89-Azja7Sfg JNTP-ThreadID: 4YLc1knY-8u5i_KQ0oWqy89D7aY JNTP-Uri: http://news2.nemoweb.net/?DataID=jiByUg3itYlr4c-5gc54C5DtzYc@jntp User-Agent: Nemo/0.999a JNTP-OriginServer: news2.nemoweb.net Date: Sun, 07 Apr 24 08:32:48 +0000 Organization: Nemoweb JNTP-Browser: Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/123.0.0.0 Safari/537.36 Injection-Info: news2.nemoweb.net; posting-host="bb35312969355368e308a66234570595632ccd80"; logging-data="2024-04-07T08:32:48Z/8808394"; posting-account="217@news2.nemoweb.net"; mail-complaints-to="julien.arlandis@gmail.com" JNTP-ProtocolVersion: 0.21.1 JNTP-Server: PhpNemoServer/0.94.5 MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit X-JNTP-JsonNewsGateway: 0.96 From: WM Bytes: 2663 Lines: 27 Le 06/04/2024 à 22:03, Richard Damon a écrit : > On 4/6/24 3:40 PM, WM wrote: >> Le 06/04/2024 à 15:58, Richard Damon a écrit : >>> On 4/6/24 9:55 AM, WM wrote: >> >>>> That mapping is Cantor's proposal. But for every other mapping, the >>>> O's would also remain. All O's! It is th lossless exchange which >>>> proves it. >>> >>> Cantor's proposal is between members of two distinct sets. >> >> No. He does not specify that. And there is no reason to do so, except >> that it can be used to contradict the ridiculous nonsense that there are >> as many fractions as prime numbers.y > > But he DOES, as he talks about the two SETS of numbers that are matched up. One set and its subset. Dedekind: A system S is said to be /infinite/ if it is similar to a real part of itself. To consider them as two sets does not change the numbers of elements. > > And yes, the size of the set of all fractions is EXACTLY of the same > size as the set of all Prime Numbers, and that size is Aleph_0. Wrong. Proof: All prime numbers p are fractions p/1 ∈ ℚ, but 1/2 is not prime. Regards, WM