Path: ...!weretis.net!feeder9.news.weretis.net!news.quux.org!eternal-september.org!feeder2.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: WM <wolfgang.mueckenheim@tha.de> Newsgroups: sci.logic Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary) Date: Wed, 13 Nov 2024 17:14:02 +0100 Organization: A noiseless patient Spider Lines: 20 Message-ID: <vh2j89$29gco$1@dont-email.me> References: <vg7cp8$9jka$1@dont-email.me> <0e67005f-120e-4b3b-a4d2-ec4bbc1c5662@att.net> <vga5mb$st52$1@dont-email.me> <vga7qi$talf$1@dont-email.me> <03b90d6c-fff1-411d-9dec-1c5cc7058480@tha.de> <vgb1fj$128tl$1@dont-email.me> <vgb2r6$11df6$3@dont-email.me> <vgcs35$1fq8n$1@dont-email.me> <vgfepg$22hhn$1@dont-email.me> <vgg0ic$25pcn$1@dont-email.me> <vggai3$25spe$8@dont-email.me> <vgi0t7$2ji2i$1@dont-email.me> <vgiet5$2l5ni$1@dont-email.me> <vgl2hj$3794c$1@dont-email.me> <vgleau$bi0i$2@solani.org> <vgnq3i$3qgfe$1@dont-email.me> <vgoka6$3vg2p$1@dont-email.me> <vgq1cm$b5vj$1@dont-email.me> <vgq3ca$beif$1@dont-email.me> <vgsp1c$v1ss$1@dont-email.me> <vgsq2v$v5t1$1@dont-email.me> <vgvm6h$1k8co$1@dont-email.me> <vgvmvr$1kc5f$1@dont-email.me> <vh1vlb$25kic$1@dont-email.me> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Wed, 13 Nov 2024 17:14:01 +0100 (CET) Injection-Info: dont-email.me; posting-host="61ce7dd57b35d31e814e3d7fc6bc44a6"; logging-data="2408856"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1+bkE4DAPNfeISTCcLnwkTg12FgX/Bwqt4=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:i2fWh92+f8U8UlM0lkvtFLFfCrA= Content-Language: en-US In-Reply-To: <vh1vlb$25kic$1@dont-email.me> Bytes: 2662 On 13.11.2024 11:39, Mikko wrote: > On 2024-11-12 13:59:24 +0000, WM said: >> Cantor said that all rationals are within the sequence and hence >> within all intervals. I prove that rationals are in the complement. > > He said that about his sequence and his intervals. Infinitely many of them > are in intervals that do not overlap with any of your J(n). The intervals J(n) = [n - 1/10, n + 1/10] cover the relative measure 1/5 of ℝ+. By translating them to match Cantor's intervals they cover ℝ+ infinitely often. This is impossible. Therefore set theorists must discard geometry. Further all finitely many translations maintain the original relative measure. The sequence 1/5, 1/5, 1/5, ... has limit 1/5 according to analysis. Therefore set theorists must discard analysis. Regards, WM