Path: ...!eternal-september.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: Fri, 3 Jan 2025 18:12:52 +0100 Organization: A noiseless patient Spider Lines: 12 Message-ID: References: <45a632ed-26cc-4730-a8dd-1e504d6df549@att.net> <3d2fe306aa299bc78e94c14dadd21645d8db9829@i2pn2.org> <2163aa0c0efba66c813e8ebda5ef5ece6d19ea34@i2pn2.org> <4441753d454842cfa2efde51b362ca5d36937a48@i2pn2.org> <2a9ace418f6cb97706e63eb54ed6ad773a09a36a@i2pn2.org> <4305026e699bfc557f4bd7c2a0d32330f3ae0b3d@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Fri, 03 Jan 2025 18:12:52 +0100 (CET) Injection-Info: dont-email.me; posting-host="01d51636a443c1100d6c37c2b77ce98b"; logging-data="4182087"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX19HQdOrraCVLwCAHN9D5RU4poqO3mYm0ws=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:hm2pyvPLaZa52IEW4Rm2TD4QOm0= In-Reply-To: <4305026e699bfc557f4bd7c2a0d32330f3ae0b3d@i2pn2.org> Content-Language: en-US Bytes: 2348 On 03.01.2025 15:49, Richard Damon wrote: > But the members taken collectively *IS* the set. Yes. The members taken individually are lacking great parts of the set. ∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo ℕ \ {1, 2, 3, ...} = { } Regards, WM