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Failed to connect to MySQL: (1203) User howardkn already has more than 'max_user_connections' active connectionsPath: ...!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: Mon, 16 Dec 2024 09:59:25 +0100 Organization: A noiseless patient Spider Lines: 20 Message-ID: References: <0b1bb1a1-40e3-464f-9e3d-a5ac22dfdc6f@tha.de> <95183b4d9c2e32651963bac79965313ad2bfe7e8@i2pn2.org> <33512b63716ac263c16b7d64cd1d77578c8aea9d@i2pn2.org> <67e587a384538d7d311613630232bf025415e67b@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Mon, 16 Dec 2024 09:59:25 +0100 (CET) Injection-Info: dont-email.me; posting-host="8cb16b437f3efafb0eb1892e9ae812c7"; logging-data="1104912"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1+GTH0KXHmZ9/6Qfa8+JrbcqFzI6DedRiA=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:hJrDPZ+jevWXRQsprVy0K6gydbI= In-Reply-To: <67e587a384538d7d311613630232bf025415e67b@i2pn2.org> Content-Language: en-US Bytes: 2648 On 15.12.2024 22:14, Richard Damon wrote: > On 12/15/24 2:44 PM, WM wrote: >> On 15.12.2024 13:54, Richard Damon wrote: >>> >>> You can't "name" your dark numbers, >> >> because they are dark. >> |ℕ \ {1, 2, 3, ...}| = 0 cannot be accomplished by visible numbers >> because ∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo. > Which just shows that the full set in infinte, and any member in it is > finite, and not the last member. Many members can be subtracted individually but infinitely many members cannot be subtracted individually. They are belonging to the set. They are dark. Regards, WM