Path: ...!weretis.net!feeder9.news.weretis.net!news.quux.org!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: "Chris M. Thomasson" Newsgroups: sci.math Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary) Date: Thu, 12 Dec 2024 18:35:06 -0800 Organization: A noiseless patient Spider Lines: 41 Message-ID: References: <3af23566-0dfc-4001-b19b-96e5d4110fee@tha.de> <8a53c5d4-4afd-4f25-b1da-30d57e7fe91c@att.net> <10ebeeea-6712-4544-870b-92803ee1e398@att.net> <1f1a4089-dfeb-45f8-9c48-a36f6a4688fb@att.net> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 7bit Injection-Date: Fri, 13 Dec 2024 03:35:06 +0100 (CET) Injection-Info: dont-email.me; posting-host="26a19b1a37777dfd496148d33b3a5183"; logging-data="3227595"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX18XnHblqjToV60cpn9Z3I3DGCQ10gG/LIc=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:90NgXfZ+mSftDzBocf0UVy2hNKw= Content-Language: en-US In-Reply-To: Bytes: 3141 On 12/10/2024 1:12 PM, Moebius wrote: > Am 10.12.2024 um 22:09 schrieb Chris M. Thomasson: >> On 12/10/2024 12:20 PM, Moebius wrote: >>> Am 10.12.2024 um 20:31 schrieb Chris M. Thomasson: >>>> On 12/10/2024 1:06 AM, Moebius wrote: >>>>> Am 09.12.2024 um 23:21 schrieb Chris M. Thomasson: >>>>>> On 12/9/2024 2:13 PM, WM wrote: >>>>>>> On 09.12.2024 23:05, FromTheRafters wrote: >>>>>>>> WM presented the following explanation : >>>>> >>>>>>>>> In sequences of sets only sets matter. >>>>> >>>>> Or rather _their contents_. >>>>> >>>>>>>> Then why are you averse to the empty set? >>>>>>> >>>>>>> Not at all! It proves the existence of dark numbers. >>>>>> >>>>>> Yawn... >>>>> >>>>> Well, the empty set contains each and every dark number, that's for >>>>> sure! >>>> >>>> { } = infinite dark? >>> >>> Nope. Actually, >>> >>> for all x: If x is a dark number, then x is in {}. >>> >>> See?! >> >> Shit. So, any natural number that WM cannot think of is dark? I guess. > > Who knows? It's complicated. :-P > > :-) > > > Yikes!