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Failed to connect to MySQL: (1203) User howardkn already has more than 'max_user_connections' active connectionsPath: ...!3.eu.feeder.erje.net!feeder.erje.net!fdn.fr!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: <7IOaykTbfjXdA1AMOzAEFksmqwU@jntp> <206ac30e-6ba5-46f2-978e-59182f946547@att.net> Newsgroups: sci.math JNTP-HashClient: mQ7FDcbMwTxAP_pOG2ynTQtmvHA JNTP-ThreadID: 0JbXgoRqYUfKvvWhEBWZVJgnda4 JNTP-Uri: http://news2.nemoweb.net/?DataID=ua_dk69eQeSqktCTQNG3SNIblRg@jntp User-Agent: Nemo/0.999a JNTP-OriginServer: news2.nemoweb.net Date: Thu, 04 Jul 24 13:49:47 +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="2024-07-04T13:49:47Z/8931954"; 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: 3362 Lines: 49 Le 04/07/2024 à 05:20, Jim Burns a écrit : > On 7/3/2024 4:00 PM, WM wrote: >> But it is impossible to >> construct or define or find or recognize or communicate >> a non-terminating decimal without using a finite formula, >> and be it as simple as "0.111...". > > Answer the questions > "What is a non.terminating.decimalⁿᵒᵗᐧᵂᴹ?" and > "What is a line.pointⁿᵒᵗᐧᵂᴹ?" > and one can prove from very reasonable assumptions > that non.terminating.decimalsⁿᵒᵗᐧᵂᴹ _exist_ > and line.pointsⁿᵒᵗᐧᵂᴹ _exist_ > and > a non.terminating.decimalⁿᵒᵗᐧᵂᴹ determines > no less than one real number (line.pointⁿᵒᵗᐧᵂᴹ) and > no more than one real number (line.pointⁿᵒᵗᐧᵂᴹ). Yes, the line point is the limit of an infinite sequence. Example: 0.999... --> 1. But the sequence cannot be given other than by its defining formula like "0.999...". > > If it is impossible to constructᵂᴹ or defineᵂᴹ or findᵂᴹ or > recognizeᵂᴹ or communicateᵂᴹ a > non.terminating.decimalⁿᵒᵗᐧᵂᴹ It is not impossible to construct every desired digit of the sequence. But it is impossible to do so without a finite formula. And it is impossible to desire all digits. ℵo are always missing. >> because it cannot be handled with enough precision. > > Then it _exists_ and is unable to be > handled.with.enough.precisionᵂᴹ. It is handled by a formula, sometimes even with absolute precision like 0.999... --> 1. > >> Always almost all digits are dark. > > All.nonempty.digit.setsⁿᵒᵗᐧᵂᴹ hold a first member. > All.digitsⁿᵒᵗᐧᵂᴹ have a first.after.digit Most are unknown. Regards, WM