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Path: ...!weretis.net!feeder8.news.weretis.net!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: Moebius <invalid@example.invalid> Newsgroups: sci.logic,sci.math Subject: Re: Replacement of Cardinality (infinite middle) Date: Sat, 10 Aug 2024 00:31:26 +0200 Organization: A noiseless patient Spider Lines: 27 Message-ID: <v965bu$75n8$1@dont-email.me> References: <hsRF8g6ZiIZRPFaWbZaL2jR1IiU@jntp> <IzWzFdkkm97GEXyAioF3IpRiSfI@jntp> <42d2b329-5394-47e0-b8c9-098908b2e9a8@att.net> <__cCn6h6Ey1Kz0BrIf6EShypg4M@jntp> <e8a3a66a-7d83-4658-9f4c-23d7dc354fb9@att.net> <iqelfxYKWhBbwcm10DcO5hr3scI@jntp> <f920592b-897c-48b9-a9af-80f25bc60e4b@att.net> <DDPks1ynTy6IhIWNHaxt25GM1v0@jntp> <c1f0efc8-04ca-4f2d-9820-cfd54c0eca73@att.net> <v90rp5$3dbpd$1@dont-email.me> <L8Pl0ELcnLfKVO0KrMmhSqDd-Y0@jntp> <v926ot$3tjq6$1@dont-email.me> <PbydnQO1H-qe_yj7nZ2dnZfqnPqdnZ2d@giganews.com> <ee820ddc-69fb-49fb-8a7c-409ecfdf25ca@att.net> Reply-To: invalid@example.invalid MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Sat, 10 Aug 2024 00:31:27 +0200 (CEST) Injection-Info: dont-email.me; posting-host="8cf6e170d08e605addc61243abfaaf20"; logging-data="235240"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX18oJ5X9kS81U5x8znTkmJE0" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:1TAgrU396PBeoeD76Qj4uzJHNiQ= In-Reply-To: <ee820ddc-69fb-49fb-8a7c-409ecfdf25ca@att.net> Content-Language: de-DE Bytes: 2517 Am 09.08.2024 um 06:01 schrieb Jim Burns: > On 8/8/2024 8:26 PM, Ross Finlayson wrote: >> 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 Great, so there are infinitely many unit fractions in (0, 1]. Right. But then for each and every x > 0 there are INFINITELY MANY unit fractions smaller than x, SINCE there are ONLY FINITELY MANY unit fractins >= x. @WM: oo - n = oo (for each and every n e IN). Kapierst Du wenigstens DAS, Mückenheim?