Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: WM Newsgroups: sci.logic Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary) Date: Sun, 15 Dec 2024 20:44:23 +0100 Organization: A noiseless patient Spider Lines: 18 Message-ID: References: <0b1bb1a1-40e3-464f-9e3d-a5ac22dfdc6f@tha.de> <95183b4d9c2e32651963bac79965313ad2bfe7e8@i2pn2.org> <33512b63716ac263c16b7d64cd1d77578c8aea9d@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Sun, 15 Dec 2024 20:44:24 +0100 (CET) Injection-Info: dont-email.me; posting-host="183e791f780bef0461f3ddd5d4b33261"; logging-data="717624"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/K6+DJTsPtwsMV6d1W78RH5sbogonCJWc=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:8CwJyRNlubKne7yJ/pm3cHDgq9g= Content-Language: en-US In-Reply-To: Bytes: 2451 On 15.12.2024 13:54, Richard Damon wrote: > > You can't "name" your dark numbers, because they are dark. > You already admitted that the set of definable natural numbers was in > fact the set of all natural numbers, No. > so there is nothing left to be dark |ℕ \ {1, 2, 3, ...}| = 0 cannot be accomplished by visible numbers because ∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo. Regards, WM