Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: FromTheRafters Newsgroups: sci.logic,sci.math Subject: Re: Replacement of Cardinality Date: Tue, 20 Aug 2024 17:25:39 -0400 Organization: Peripheral Visions Lines: 20 Message-ID: References: <9ef8dd8a-69be-44e2-bcf6-ea9c1fb30e21@att.net> <92189533-0c1f-4532-816f-564651cc8bf7@att.net> <155cdc8a628d47be1632791227bccf99425b1d5e@i2pn2.org> Reply-To: erratic.howard@gmail.com MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-15"; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Tue, 20 Aug 2024 23:25:44 +0200 (CEST) Injection-Info: dont-email.me; posting-host="b62d911f8037ccb2d638782bbebed3a6"; logging-data="3714037"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/SsETUOJCSC1jhH4oPHyC+ZymdFzm7as0=" Cancel-Lock: sha1:LcQ/sI8wqCQ6ULuvDVRCTuCequc= X-Newsreader: MesNews/1.08.06.00-gb X-ICQ: 1701145376 Bytes: 2206 WM explained : > Le 20/08/2024 à 12:31, FromTheRafters a écrit : >> on 8/19/2024, Richard Damon supposed : > >>> You can not derive a first number > 0 in any of the Number System that we >>> have been talking about, Unit Fractions, Rationals or Reals, so you can't >>> claim it to exist. >> >> Not in their natural ordering. > > Dark numbers have no discernible order. It is impossible to find the smallest > unit fraction or the next one or the next one. It is only possible to prove > that NUF(x) grows by 1 at every unit fraction. It starts from 0. > > Regards, WM Normally, the unit fractions are listed in the sequence one over one, one over two, one over three etcetera. There is a first but no last. Now you have started from the wrong 'end' and are metaphorically pushing a rope.