Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: Keith Thompson Newsgroups: comp.theory Subject: Re: Repeating decimals are irrational Date: Tue, 26 Mar 2024 17:28:32 -0700 Organization: None to speak of Lines: 68 Message-ID: <8734scv7pr.fsf@nosuchdomain.example.com> References: <87wmppuhn8.fsf@nosuchdomain.example.com> <87sf0dueli.fsf@nosuchdomain.example.com> <27544510d7559860979611a504b6ad0d9aebfd1c.camel@gmail.com> <87o7b0vja4.fsf@nosuchdomain.example.com> <1b980d564d961c4c290b5bf722835f2f2f284969.camel@gmail.com> <87jzloveiw.fsf@nosuchdomain.example.com> <87frwcvc19.fsf@nosuchdomain.example.com> <02aa964280a00d97c3d3d23af84f5582d5497ff7.camel@gmail.com> <87bk70varb.fsf@nosuchdomain.example.com> <877chov8yo.fsf@nosuchdomain.example.com> <25b8768c198e38ab7e7a3f318afb4b8dbc37f4aa.camel@gmail.com> MIME-Version: 1.0 Content-Type: text/plain; charset=utf-8 Content-Transfer-Encoding: 8bit Injection-Date: Wed, 27 Mar 2024 00:28:33 +0100 (CET) Injection-Info: dont-email.me; posting-host="be872d10ee262eeda162bfc9b99446ee"; logging-data="2568808"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX18LVntHyVjEG0mNQ+6vXiNt" User-Agent: Gnus/5.13 (Gnus v5.13) Emacs/27.2 (gnu/linux) Cancel-Lock: sha1:ifJYgieeJP2bXXyHWcJmyu20mPA= sha1:JVktpfAlYPKwsqM1Y5EEUIWQp9U= Bytes: 4305 wij writes: > On Tue, 2024-03-26 at 17:01 -0700, Keith Thompson wrote: >> wij writes: >> > On Tue, 2024-03-26 at 16:22 -0700, Keith Thompson wrote: >> > > wij writes: >> > > > On Tue, 2024-03-26 at 15:55 -0700, Keith Thompson wrote: >> > > [...] >> > > > > Do you understand what a mathematical limit is?  Can you explain it? >> > > > > >> > > > > If you understand limits, you should be able to understand that >> > > > > 0.333..., where the "..." denotes the limit as the number of 3s exceeds >> > > > > without bound, is exactly equal to 1/3. >> > > > > >> > > > > [...] >> > > > > >> > > > >> > > > I already stated it the file: >> > > > https://sourceforge.net/projects/cscall/files/MisFiles/RealNumber-en.txt/download >> > > >> > > OK, in that file you wrote: >> > > >> > >     Ex1: A= lim(n->∞) 1-1/n= lim(n->0⁺) 1-n= lim 0.999...=1 >> > >          B= lim(n->∞) 1+1/n= lim(n->0⁺) 1+n= lim 1.000..?=1 >> > > >> > > What do you mean by that question mark?  Do you agree that both limits >> > > in your example (A and B) are equal to 1? >> > > >> > >> > Agree. >> >> OK.  Do you agree that 0.333..., where ... denotes the limit as the >> number of 3s increases without bound, is exactly equal to 1/3? >> > > Nop. I'll assume that's a typo for "No" or "Nope". So you're saying that 0.333... is not exactly equal to 1/3. It seems odd that you agree that 0.999... is exactly equal to 1, but 0.333... is not exactly equal to 1/3. Is 0.333... a real number? Is 1/3 - 0.333... a real number? What is the value of 1/3 - 0.333...? >> And that that number multipled by 3 is exactly equal to 1? >> >> And that 0.999... is exactly equal to 1? >> >> And that all the numbers we're discussing are both real and rational? > > Can you make statement really like math? Please rephrase that. I don't understand what it means. > You still keep asserting your belief, not a proof but strangely formed statement !!! > You cannot read proof !!! Go home and learn more. I haven't offered a proof because (a) there's no point in doing so if we don't have enough mutual understanding, and (b) I'm not a mathematician, so I'm not confident of my ability to construct a rigorous proof. I might give it a try later, but I see no point in doing so now. -- Keith Thompson (The_Other_Keith) Keith.S.Thompson+u@gmail.com Working, but not speaking, for Medtronic void Void(void) { Void(); } /* The recursive call of the void */