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Path: ...!2.eu.feeder.erje.net!3.eu.feeder.erje.net!feeder.erje.net!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: WM <wolfgang.mueckenheim@tha.de> Newsgroups: sci.math Subject: Re: quantifier order Date: Tue, 10 Sep 2024 18:24:25 +0200 Organization: A noiseless patient Spider Lines: 15 Message-ID: <vbprro$31fu6$5@dont-email.me> References: <vb4rde$22fb4$2@solani.org> <vbd56i$fqa0$1@dont-email.me> <vbdbq3$gdoe$2@dont-email.me> <vbes57$qdqo$2@dont-email.me> <27b3b5e088d82d4475c68a64f50a4bccac9c6f29@i2pn2.org> <vbesjo$27gfe$1@solani.org> <vbf0s9$qp1j$3@dont-email.me> <vbfpf5$utdu$2@dont-email.me> <vbh5qe$19a45$1@dont-email.me> <vbhdf6$1btm1$1@dont-email.me> <vbhdsh$1btm1$2@dont-email.me> <vbhj65$1bi3k$3@dont-email.me> <9eeba8a5041ce7ee48e5019d9e98d4ea38a1eb72@i2pn2.org> <vbhkmo$1bi3l$8@dont-email.me> <89ed6d8de6c20d65e869d384181b642309f63bc4@i2pn2.org> <vbkv1r$20uoi$4@dont-email.me> <7a991922c09e309450ac278f884091dfe716cae3@i2pn2.org> <vbmij2$2ce0a$4@dont-email.me> <918c948309b4a74d0bc505a1c2f40a7868072f41@i2pn2.org> <vbn25d$2em18$1@dont-email.me> <4f9cb578fe0b0891c115fd21cbc25642f706b63a@i2pn2.org> <83d741b4-a0bc-42f3-a286-9d26d164ff66@tha.de> <c98febf86c866fab791406bc6769aef26a7bd29d@i2pn2.org> <vbngps$2gn74$2@dont-email.me> <2e31239990bdcbe4ce41a3b9a2e17859d4c3e438@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 7bit Injection-Date: Tue, 10 Sep 2024 18:24:25 +0200 (CEST) Injection-Info: dont-email.me; posting-host="49ad7ab0efe8995e55f8413a9208187f"; logging-data="3194822"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/ZjID0BOC4hgucPJaBGC6Jx0qNgdp4L88=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:03jkIUocrCnBHkLwTncrPYtXFhU= In-Reply-To: <2e31239990bdcbe4ce41a3b9a2e17859d4c3e438@i2pn2.org> Content-Language: en-US Bytes: 2541 On 09.09.2024 21:55, joes wrote: > Am Mon, 09 Sep 2024 21:03:24 +0200 schrieb WM: >> On 09.09.2024 17:49, joes wrote: >> No, that is THE question. > The set of unit fractions smaller than all x is empty. Why is this so? Because all unit fractions are undercut by some x. The x undercutting the last unit fractions (you said that none remains because the set is empty, therefore all must be gone) do not satisfy your following claim: > However, the set of UFs smaller than one arbitrary x is infinite. Regards, WM