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 (infinite middle) Date: Fri, 09 Aug 2024 06:25:20 -0400 Organization: Peripheral Visions Lines: 21 Message-ID: References: <42d2b329-5394-47e0-b8c9-098908b2e9a8@att.net> <__cCn6h6Ey1Kz0BrIf6EShypg4M@jntp> 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: Fri, 09 Aug 2024 12:25:27 +0200 (CEST) Injection-Info: dont-email.me; posting-host="810fb53979376775e1cf20ff6af39081"; logging-data="735830"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/0SQIQRI5EJwl1viqoVKXpS5q2CfnbT0g=" Cancel-Lock: sha1:CpKlh5z4CJCuD10mmItI0L8LXc8= X-ICQ: 1701145376 X-Newsreader: MesNews/1.08.06.00-gb Bytes: 2227 Ross Finlayson explained : > On 08/08/2024 03:30 AM, FromTheRafters wrote: >> on 8/8/2024, WM supposed : >>> Le 08/08/2024 à 00:17, Moebius a écrit : >>> >>>> Actually, his "thinking process" is simple: >>>> >>>> "Since there is a gap (space) between adjacent unit fractions and all >>>> unit fractions are in the interval (0, 1], there must be FINITELY >>>> MANY of them (i.e. a first/smallest one)." >>> >>> No, that is nonsense. There are not finitely many unit fractions. >> >> Then stop assuming that there is a first and last element. > > Of course, you can start with a first and last element, > then make infinitely-many in the middle. > > 0 ... ( ... infinitely-many ... ) ... infinity Sometimes you are as bad as he is. :)