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Failed to connect to MySQL: (1203) User howardkn already has more than 'max_user_connections' active connectionsPath: ...!local-1.nntp.ord.giganews.com!Xl.tags.giganews.com!local-4.nntp.ord.giganews.com!news.giganews.com.POSTED!not-for-mail NNTP-Posting-Date: Tue, 15 Oct 2024 18:29:08 +0000 Subject: Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Newsgroups: sci.math References: <4bc3b086-247a-4547-89cc-1d47f502659d@tha.de> <3f5fcf13171337f1c3d2ef84cc149be327648451@i2pn2.org> <97b84c07aa526903a0788584f7f7ae9121f8b81f@i2pn2.org> <60f1280e-e226-4314-8eca-da5410be8ca3@tha.de> <96a7aa944085e76faed69c8db9a8dca599e1a159@i2pn2.org> <2c732eefb860986209bd46ed88391ddceaddff55@i2pn2.org> From: Ross Finlayson Date: Tue, 15 Oct 2024 11:29:25 -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: <2c732eefb860986209bd46ed88391ddceaddff55@i2pn2.org> Content-Type: text/plain; charset=utf-8; format=flowed Content-Transfer-Encoding: 8bit Message-ID: Lines: 29 X-Usenet-Provider: http://www.giganews.com X-Trace: sv3-aKzAfOf9B2W/3mqv/x1dXNWyCUiCpAVZwSGiLKg4/JdsUxZM2qOz1mnnFpNBuFnBFGUNpBOBBPewx/F!6jFwLmIUF1kUZM/dqkWe/P8P5SsLLA7V6yOiY9Nc1ws3KgLYnn+6YltAPCZT7MfSNHnL0XScQA0c!ow== 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: 3408 On 10/15/2024 08:51 AM, joes wrote: > Am Mon, 14 Oct 2024 18:37:31 +0200 schrieb WM: >> On 14.10.2024 18:04, joes wrote: >>> Am Mon, 14 Oct 2024 15:40:01 +0200 schrieb WM: >>>> On 14.10.2024 14:15, joes wrote: >>>> >>>>> No, we are taking the complete, actually infinite set which reaches >>>>> to "before" w. >>>> and fills the space between 0 and ω evenly. Same happens with the >>>> doubled set between 0 and ω2. >>> No, there is no consequent infinity. The even numbers do not go 0, 2, >>> 4, ..., w, w+2, w+4, ..., w*2 >> Either the doubled numbers are natural, then half of them have not been >> among the original set, or all natural numbers have been doubled, then >> the result contains infinite numbers. > Which "half"? > >> That doubling _all_ natural numbers only yields _all_ natural numbers is >> impossible. > Of course. But all doubled naturals are themselves natural. > Aliquot parts, i.e. density where the "half of the integers are even", and the equivalency of the countably infinite, where "integers are 1-1 squares" were around centuries and THOUSANDS of years before Grosseteste and Galileo, and are such OLD HAT that this "old wrapped as new" is long, long, long past its freshness dating.