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Path: 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 18:55:15 +0100 Organization: A noiseless patient Spider Lines: 19 Message-ID: <vggai3$25spe$8@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> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Wed, 06 Nov 2024 18:55:15 +0100 (CET) Injection-Info: dont-email.me; posting-host="fa4d81affe87dc195ff2c4aafd71ec8e"; logging-data="2290478"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1+apDAT7xGrnEDLA0PUY+O2WcXZhMv7ADc=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:ZxwjA69PYM3ZkGFMwywto75syeQ= In-Reply-To: <vgg0ic$25pcn$1@dont-email.me> Content-Language: en-US On 06.11.2024 16:04, Mikko wrote: > On 2024-11-06 10:01:21 +0000, WM said: >> I leave ε = 1. No shrinking. Every point outside of the intervals is >> nearer to an endpoint than to the contents. > > This discussion started with message that clearly discussed limits when > ε approaches 0. The case ε = 1 was only about a specific unimportant > question. When ε approaches 0 then the measure of the real axis is, according to Cantor's results, 0. That shows that his results are wrong. But the important question is also covered by ε = 1. The measure of the real axis is, according to Cantor's results, less than 3. That shows that his results are wrong. Regards, WM