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Path: ...!news.mixmin.net!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: FromTheRafters <FTR@nomail.afraid.org> Newsgroups: sci.math Subject: Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Date: Sun, 20 Oct 2024 07:20:29 -0400 Organization: Peripheral Visions Lines: 27 Message-ID: <vf2p1v$d2bb$1@dont-email.me> References: <vb4rde$22fb4$2@solani.org> <veirkn$desj$2@solani.org> <db221d267ae4b956cd0818c9b5ccc0311df97d1e@i2pn2.org> <60f1280e-e226-4314-8eca-da5410be8ca3@tha.de> <96a7aa944085e76faed69c8db9a8dca599e1a159@i2pn2.org> <vejhcb$ditg$1@solani.org> <2c732eefb860986209bd46ed88391ddceaddff55@i2pn2.org> <vOmcnYVG-OHpKZP6nZ2dnZfqnPSdnZ2d@giganews.com> <avecnXK3J6VsU5P6nZ2dnZfqnPhg4p2d@giganews.com> <vensvb$2533b$2@dont-email.me> <veoumv$2bc1q$4@dont-email.me> <veovbm$2bc2g$2@dont-email.me> <aqCcnTFQ7MNz_436nZ2dnZfqnPudnZ2d@giganews.com> <bd2fe5d4-c284-47e7-a265-720539d2ab42@att.net> <27WcnWnC9tjPyIz6nZ2dnZfqn_idnZ2d@giganews.com> <f1e485be-dc79-49ba-87fa-4bb23910d878@att.net> <4d080bc4-7c84-4951-a8f4-9bf0f95ad47f@tha.de> <dcd6560e-e5cc-4c14-8607-c32977f6c622@att.net> <vf042r$3rmh1$1@dont-email.me> <c3993c0d-1904-4b7e-ae45-cf2651cc5eb0@att.net> <vf0tno$6c6$1@dont-email.me> <2f1438e0-4b73-474c-afe6-f8dcb1b71743@att.net> <vf2c55$ambv$2@dont-email.me> Reply-To: erratic.howard@gmail.com MIME-Version: 1.0 Content-Type: text/plain; charset="utf-8"; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Sun, 20 Oct 2024 13:20:31 +0200 (CEST) Injection-Info: dont-email.me; posting-host="0703cd44d0473c7f6a65a7d1771cecfa"; logging-data="428395"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1+T+LBlJVombc/sPnxPuFyt/bQ+ft4VABg=" Cancel-Lock: sha1:DW81RFj3tMU6ZdhimU0yPiiLvxE= X-Newsreader: MesNews/1.08.06.00-gb X-ICQ: 1701145376 Bytes: 2701 WM was thinking very hard : > On 20.10.2024 00:08, Jim Burns wrote: >> On 10/19/2024 2:28 PM, WM wrote: > >>> >>> The contradiction is independent of infinity. >>> It is your claim that >> >> infinitely.many exchanges in an infinite set >> (vanishing Bob) > > Every exchange is _one_ lossless exchange. >> >>> exchanging two objects >>> can result in the loss of one of them. >> >> I fixed that for you. > > It is nonsense like: > ∀n ∈ ℕ: |{2, 4, 6, ..., 2n}|/|{1, 2, 3, 4, 5, 6, ..., 2n} = 1/2 > but |{2, 4, 6, ...}|/|{1, 2, 3, 4, 5, 6, ...} = 1. You made some typos here. You left out a couple of "|" for the cardinalities. Plus, how do you define division on cardinalities -- especially the infinite ones?