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Failed to connect to MySQL: (1203) User howardkn already has more than 'max_user_connections' active connectionsPath: ...!news.mixmin.net!weretis.net!feeder8.news.weretis.net!reader5.news.weretis.net!news.solani.org!.POSTED!not-for-mail From: WM Newsgroups: sci.math Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers Date: Wed, 27 Nov 2024 20:15:34 +0100 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 19:15:34 -0000 (UTC) Injection-Info: solani.org; logging-data="527079"; mail-complaints-to="abuse@news.solani.org" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:gDMXSh+xCE6mTFAg+ckxuKMhee4= Content-Language: en-US In-Reply-To: X-User-ID: eJwFwQcBwDAMAzBKeXYaOOsxfwiTkHSeLoIFQcIz5Ozl+xjWfu5nfJk0wfS4t9g+mGpazxeRisb9eCnZ+wE1+hSy Bytes: 2524 Lines: 16 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. > It it the successor for the SET of natural numbers. And that is nothing else but all natural numbers. Regards, WM