Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: Moebius Newsgroups: sci.math Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary) Date: Tue, 24 Dec 2024 01:03:21 +0100 Organization: A noiseless patient Spider Lines: 34 Message-ID: References: <3c08ed64fa6193dc9ab6733b807a5c99a49810aa@i2pn2.org> <357a8740434fb6f1b847130ac3afbd33c850fc37@i2pn2.org> <787067e5de3c455cb57389315b6821e96bcf86af@i2pn2.org> <1b6f89e7c35e4c9674af5a480e4bab6cb72e0915@i2pn2.org> <733ce219e9d2422859035e5094a7b3e92eea9c47@i2pn2.org> Reply-To: invalid@example.invalid MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Tue, 24 Dec 2024 01:03:21 +0100 (CET) Injection-Info: dont-email.me; posting-host="a9b2b0b8368e7a8d7336b1cdb87f7350"; logging-data="1528890"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX18QuAyzl0H3roHNEZxhqXEE" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:Y4fT7bsNNuvUiKOQ3uGTtCYPIhg= Content-Language: de-DE In-Reply-To: Bytes: 3063 Am 24.12.2024 um 00:56 schrieb Moebius: > Am 24.12.2024 um 00:49 schrieb Chris M. Thomasson: >> On 12/23/2024 6:32 AM, Richard Damon wrote: >>> On 12/23/24 4:31 AM, WM wrote: >>>> On 23.12.2024 02:01, Richard Damon wrote: >>>>> On 12/22/24 5:11 PM, WM wrote: >>>>>> On 22.12.2024 20:10, Richard Damon wrote: >>>>>>> On 12/22/24 8:11 AM, WM wrote: >>>>>> >>>>>>>> Find a natural number that is not in all intervals [1, n] which >>>>>>>> I use: ∀n ∈ ℕ [1, n]. >>>>>>> >>>>>>> But you can't use *ALL* intervals, becaue you need to use them >>>>>>> individually >>>>>> >>>>>> No, I do as Cantor did. >>>> >>>>> No, you do what you THINK Cantor did, >>>> >>>> Show an n that I do not use with all intervals [1, n]. >>> >>> The LAST one, which you say must exist to use your logic. >> >> LOL! n+1? >> >> Am I close here? Or way off? > > Yeah, you are close to the edge. Hint: "It is not guaranteed that n+1 exists for every n." (WM in sci.math, 20 Jul 2024) > See: https://www.youtube.com/watch?v=51oPKLSuyQY