Path: ...!feeds.phibee-telecom.net!weretis.net!feeder8.news.weretis.net!pasdenom.info!from-devjntp Message-ID: JNTP-Route: news2.nemoweb.net JNTP-DataType: Article Subject: Re: Replacement of Cardinality References: <40165884-df8f-4614-8644-9161d72fd1cb@att.net> <-qUZ96ARwcjh9QPfyWRnijjNwoY@jntp> <6b837540-3d9a-4b8e-9a70-88d52e81a1a4@att.net> <9822f5da-d61e-44ba-9d70-2850da971b42@att.net> <4f606ef2-ef6c-487b-b959-d109e374929f@att.net> Newsgroups: sci.logic,sci.math JNTP-HashClient: fd8zOqKqpeNjkv9Pude26V0ZqvU JNTP-ThreadID: KFm3f7lT2HjaTSiMfnv5xqZoSBw JNTP-Uri: http://news2.nemoweb.net/?DataID=vpb42BOZYYy79eBYzCXpUbsjGQc@jntp User-Agent: Nemo/0.999a JNTP-OriginServer: news2.nemoweb.net Date: Sun, 04 Aug 24 15:29:07 +0000 Organization: Nemoweb JNTP-Browser: Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/127.0.0.0 Safari/537.36 Injection-Info: news2.nemoweb.net; posting-host="82b75c1d0a83e677ff646b52485f72f8b23749df"; logging-data="2024-08-04T15:29:07Z/8975314"; posting-account="217@news2.nemoweb.net"; mail-complaints-to="julien.arlandis@gmail.com" JNTP-ProtocolVersion: 0.21.1 JNTP-Server: PhpNemoServer/0.94.5 MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit X-JNTP-JsonNewsGateway: 0.96 From: WM Bytes: 2251 Lines: 24 Le 03/08/2024 à 21:54, Jim Burns a écrit : > On 8/3/2024 10:23 AM, WM wrote: >> I recognized lately that you use >> the wrong definition of NUF. >> >> Here is the correct definition: >> There exist NUF(x) unit fractions u, such that >> for all y >= x: u < y. > Here is an equivalent definition: > There exist NUF(x) unit fractions u, such that > u < x > >> Note that the order is ∃ u ∀ y. > > The order is ∀x ∃u ∀y > ∃u ∀x ∀y is an unreliable quantifier shift. It is not a shift but it is the definition of NUF. It excludes that ∃u ∀x>0: u < x, Regards, WM