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Failed to connect to MySQL: (1203) User howardkn already has more than 'max_user_connections' active connectionsPath: ...!news.misty.com!weretis.net!feeder9.news.weretis.net!news.quux.org!feeder3.eternal-september.org!news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail From: WM Newsgroups: sci.math Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary, effectively) Date: Tue, 31 Dec 2024 19:05:24 +0100 Organization: A noiseless patient Spider Lines: 45 Message-ID: References: <45a632ed-26cc-4730-a8dd-1e504d6df549@att.net> <3d2fe306aa299bc78e94c14dadd21645d8db9829@i2pn2.org> <2163aa0c0efba66c813e8ebda5ef5ece6d19ea34@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Tue, 31 Dec 2024 19:05:24 +0100 (CET) Injection-Info: dont-email.me; posting-host="f381e8cbf6f8cad106a41c0e6b63673a"; logging-data="2470684"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX180OQBmbfB25PeFWFLzfe2/hazKwxkofiM=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:hBk/ZqGELmNwOR9un0sEDs+P7E4= Content-Language: en-US In-Reply-To: <2163aa0c0efba66c813e8ebda5ef5ece6d19ea34@i2pn2.org> Bytes: 3659 On 31.12.2024 16:37, Richard Damon wrote: > On 12/30/24 4:38 PM, WM wrote: >> On 30.12.2024 17:08, Richard Damon wrote: >>> On 12/30/24 3:44 AM, WM wrote: >>>> On 30.12.2024 01:36, Richard Damon wrote: >>>>> On 12/29/24 5:31 PM, WM wrote: >>>> >>>>>> My theorem: Every union of FISONs which stay below a certain >>>>>> threshold stays below that threshold. >>>>>> Find a counterexample. Don't claim it but prove it. Fail. >>>> >>>>> But what does that prove? >>>> >>>> That proves the existence of dark numbers. >>> >>> How? >>> >>> It shows that there are numbers you didn't look at, but you admit to >>> not looking at all the numbers. >> >> Neither can you look at more numbers. > > Of course I can look at "more" numbers, as I can look at the one after > where you stopped. I don't stop but know that every FISON is finite as its name says and covers at most 1 % of ℕ. If you don't agree find a counterexample. >>>> If ℕ is an actually infinite set then it is not made by FISONs. >> >> That is what I have been telling you for a long time. > > But there is no Natural Number that isn't in a FISON, which is NOT what > you have been saying. You cannot find a natural number that isn't in a FISON. But there must be more because FISONs cover less than 1 % of ℕ. > The problem is your logic can't have "Every" FISON, because "every > FISON" is an infinite set of them, Every mathematician knows that every FISON is finite as its name says and covers at most 1 % of ℕ. Regardes, WM