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Path: ...!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, 6 Nov 2024 11:01:21 +0100 Organization: A noiseless patient Spider Lines: 21 Message-ID: <vgfepg$22hhn$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> <3wydnd-9IL2MRLf6nZ2dnZfqn_SdnZ2d@giganews.com> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Wed, 06 Nov 2024 11:01:21 +0100 (CET) Injection-Info: dont-email.me; posting-host="985d4bef482e665fd2b5ab998c67740a"; logging-data="2180663"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1+fwGZgAr0qmGHtcd0ntQm1Rukh7JhYsWM=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:6eLGPptF4uAnZRIxtZG+y36eO/Q= In-Reply-To: <3wydnd-9IL2MRLf6nZ2dnZfqn_SdnZ2d@giganews.com> Content-Language: en-US Bytes: 2146 On 06.11.2024 03:48, Ross Finlayson wrote: > On 11/05/2024 02:29 AM, Mikko wrote: >>> Geometry is only another language for the same thing. >> >> Another language is an unnecessary complication that only reeasls >> an intent to deceive. It is a clearer language. >> >> No, the meaning is clear. Of course, because some intevals overlap, >> you should have specified what exacly you mean by "nearer". But as >> ε shriks the overlappings disappear and the distance between any >> two intevals approaches the distance between their centers we may >> define distance between the intervals as the distance between their >> endpoints even wne ε > 0. I leave ε = 1. No shrinking. Every point outside of the intervals is nearer to an endpoint than to the contents. Regards, WM