Path: ...!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 Date: Wed, 27 Nov 2024 12:28:51 -0800 Organization: A noiseless patient Spider Lines: 24 Message-ID: References: <0d6d06a888e15ed2042aca8ec7e6ebb93590b7bc@i2pn2.org> <8a2aedd8383a84ceef2fd985ac0bf529e2a0eccf@i2pn2.org> <3fe6ef31f562e0ddf598de46cf864986ca909687@i2pn2.org> <9cb8aec671200bb6d71582fd607b876b7ec4c83a@i2pn2.org> <40292abc147fee5a7bdd264b69d34ddf2061e59d@i2pn2.org> <0bc3cdc8c096bba16decd94ad2af85d35da9b7b4@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Wed, 27 Nov 2024 21:28:51 +0100 (CET) Injection-Info: dont-email.me; posting-host="ce9ecf2e7ec11584eaae6495547bc79a"; logging-data="179967"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/5HwSEHJijBHTLd9JTUio/wrdgxcmvE/U=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:QVRLzPt1av9nIvmDSWz18pVg5Xg= Content-Language: en-US In-Reply-To: Bytes: 2700 On 11/27/2024 11:15 AM, WM wrote: > On 27.11.2024 18:58, Richard Damon wrote: >> On 11/27/24 12:13 PM, WM wrote: > >>> Replacing every element of the set {0, 1, 2, 3, ...} by its successor >>> yields {1, 2, 3, ..., ω}. The number of ordinals remains the same, >>> the number of finite ordinals decreases. >> >> Nope, because omega is NOT the successor for any natural number, the >> successor of EVERY Natural Number is a Natural Number. > > The successor of the last natural number is ω. There is no last natural number you fucking dipshit! > >> It it the successor for the SET of natural numbers. > > And that is nothing else but all natural numbers. > > Regards, WM