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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: Tue, 12 Nov 2024 14:59:24 +0100 Organization: A noiseless patient Spider Lines: 17 Message-ID: <vgvmvr$1kc5f$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> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 7bit Injection-Date: Tue, 12 Nov 2024 14:59:24 +0100 (CET) Injection-Info: dont-email.me; posting-host="58c87137bb70e24653c8534960defd84"; logging-data="1716399"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX18d5GI6TKB/IszL43Ek8SjqeaLBpAqcz5U=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:w39fUljl8H8U4EBQRgYf8REjsA0= Content-Language: en-US In-Reply-To: <vgvm6h$1k8co$1@dont-email.me> Bytes: 2312 On 12.11.2024 14:45, Mikko wrote: > On 2024-11-11 11:33:52 +0000, WM said: >>> Between the intervals J(n) and (Jn+1) there are infinitely many rational >>> and irrational numbers but no hatural numbers. > >> Therefore infinitely many natural numbers must become centres of >> intervals, if Cantor was right. But that is impossible. > > Where did Cantor say otherwise? Cantor said that all rationals are within the sequence and hence within all intervals. I prove that rationals are in the complement. Regards, WM