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Failed to connect to MySQL: (1203) User howardkn already has more than 'max_user_connections' active connectionsPath: ...!Xl.tags.giganews.com!local-2.nntp.ord.giganews.com!news.giganews.com.POSTED!not-for-mail NNTP-Posting-Date: Tue, 27 Aug 2024 23:41:50 +0000 Subject: Re: Replacement of Cardinality (book-keeping sign) Newsgroups: sci.math References: <980a0ec7476c9dc5823e59b2969398bd39d9b91d@i2pn2.org> <8d5b0145-b30d-44d2-b4ff-b01976f7ca66@att.net> <6cc86827-def3-4948-9e69-a3fea9e86c06@att.net> From: Ross Finlayson Date: Tue, 27 Aug 2024 16:41:55 -0700 User-Agent: Mozilla/5.0 (X11; Linux x86_64; rv:38.0) Gecko/20100101 Thunderbird/38.6.0 MIME-Version: 1.0 In-Reply-To: Content-Type: text/plain; charset=utf-8; format=flowed Content-Transfer-Encoding: 8bit Message-ID: Lines: 24 X-Usenet-Provider: http://www.giganews.com X-Trace: sv3-YeRyxB8l/5zEzkZLe1hQ8a6NVwIBN0fL/XBbGkD6SLlK+Uu+JBPouHT6uIClg3Xqf00jhb5RRMNQIfm!MABcXM5oSE8vS/abE6a4++yD/9DGCJbGDJs8Blshz5r6XBvqZ1sGeIX38RenK+PuSkOYHCFXlyKc!gA== X-Complaints-To: abuse@giganews.com X-DMCA-Notifications: http://www.giganews.com/info/dmca.html X-Abuse-and-DMCA-Info: Please be sure to forward a copy of ALL headers X-Abuse-and-DMCA-Info: Otherwise we will be unable to process your complaint properly X-Postfilter: 1.3.40 Bytes: 2339 On 08/27/2024 04:06 PM, FromTheRafters wrote: > WM wrote : >> Le 25/08/2024 à 23:18, Jim Burns a écrit : >> >>> Therefore, >>> there is no ω-1, >> >> If the set of ordinal numbers is complete, then ω-1 precedes ω - by >> definition. > > What is the definition of subtraction here? Can you subtract past zero > in the naturals? You can build a little mound out past ten, say, then relate that to zero in a sliding scale, then if you find you can't remember how to roll the clock back, you can count so many forward howsoever many were lost, with a bit of book-keeping then it so results, that the extra cost involved in counting over numbering, lets you build the integers as deep as they are.