Path: ...!news.mixmin.net!proxad.net!feeder1-2.proxad.net!usenet-fr.net!pasdenom.info!from-devjntp Message-ID: JNTP-Route: news2.nemoweb.net JNTP-DataType: Article Subject: Re: Does the number of nines =?UTF-8?Q?increase=3F?= References: <59961718-bd36-46df-801a-4f977fcc05cf@att.net> <5839EQYIqMEekW6z6mzwy1WOE0U@jntp> <1c1b71c4-b01a-4635-9b38-ff53c5a983bf@att.net> <-BnA2ysAH93IswYF0ScqxyUX-SA@jntp> <3e61967c-0d8c-4ee3-a9bd-0e5314d8d094@att.net> <0BdGVCEAFkl5VNEZByFL4v-DOcQ@jntp> Newsgroups: sci.math JNTP-HashClient: 7KJnxgDrwt_rm0O93d72gHONnp8 JNTP-ThreadID: 0JbXgoRqYUfKvvWhEBWZVJgnda4 JNTP-Uri: http://news2.nemoweb.net/?DataID=oxb2A77hW7b3tk0p1JKW7ga71l8@jntp User-Agent: Nemo/0.999a JNTP-OriginServer: news2.nemoweb.net Date: Sun, 30 Jun 24 15:18:31 +0000 Organization: Nemoweb JNTP-Browser: Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/126.0.0.0 Safari/537.36 Injection-Info: news2.nemoweb.net; posting-host="25d5a506365fc8262443ce1bd287e5d0233c1bef"; logging-data="2024-06-30T15:18:31Z/8925789"; 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: 2287 Lines: 16 Le 29/06/2024 à 22:25, joes a écrit : > Am Sat, 29 Jun 2024 17:18:26 +0000 schrieb WM: >> All nines of 0.999... are from the sequence 0.9, 0.09, 0.009, ... None >> of the ℵo nines makes its partial sum 0,9, 0.99, 0.999, ... equal to 1. >> ℵo nines fail to make 0.999... = 1. > That’s one way to construct it. Of course none of the infinite series > individually reaches the limit (otherwise the following ones :-P would go > above it?). Together they do. It is reached after exactly Aleph0 steps. Are there ℵo partial sums 0.9, 0.99, 0.999, ... ? If yes they can be combined to 0.999... . Is the limit one of them? Regards, WM