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Failed to connect to MySQL: (1203) User howardkn already has more than 'max_user_connections' active connectionsPath: ...!weretis.net!feeder9.news.weretis.net!news.quux.org!eternal-september.org!feeder2.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: WM Newsgroups: sci.math Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers Date: Mon, 18 Nov 2024 19:20:24 +0100 Organization: A noiseless patient Spider Lines: 15 Message-ID: References: <97304048-24f5-4625-82a7-d17427f2f6e3@att.net> <65febd06-662b-4fa4-9aa8-f7353a79a110@att.net> <157a949d-6c19-4693-8cee-9e067268ae45@att.net> <8165b44b-1ba5-429d-8317-0b043b214b53@att.net> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Mon, 18 Nov 2024 19:20:25 +0100 (CET) Injection-Info: dont-email.me; posting-host="4277cd5398b33328aee403404fb6cf14"; logging-data="1390252"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX193HTDWI2FxMAin+PXClEVxXjvhgjMLHE0=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:8RAP7WYnKXfCyGx5ztUmQOrXXWk= Content-Language: en-US In-Reply-To: Bytes: 2553 On 18.11.2024 18:15, FromTheRafters wrote: > WM brought next idea : >>> |ℕ| - |ℕ| = 0 because if you subtract one element from ℕ then you have >> no longer ℕ and therefore no longer |ℕ| describing it. > > Still wrong. If you remove one element from ℕ, then you have still ℵo but no longer all elements of ℕ. If |ℕ| describes the number of elements, then it has changed to |ℕ| - 1. If you don't like |ℕ| then call this number the number of natural numbers. Regards, WM