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Re: Repeating decimals are irrational

From wij <wyniijj5@gmail.com>
Newsgroups comp.lang.c++
Subject Re: Repeating decimals are irrational
Date 2024-03-29 02:23 +0800
Organization A noiseless patient Spider
Message-ID <c05df08e5d04c3b3baa1dfd36c2ed23b0c2ca535.camel@gmail.com> (permalink)
References (5 earlier) <uu152u$2qpb5$1@dont-email.me> <c256dbb376440ca8535bb27a0ecebb37304a583f.camel@gmail.com> <uu1cel$2te2i$2@dont-email.me> <435b9fe3357bbc4dd5a25f8f9e75637e270dd55b.camel@gmail.com> <uu48kk$3n14g$1@dont-email.me>

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On Thu, 2024-03-28 at 18:16 +0100, David Brown wrote:
> On 27/03/2024 17:05, wij wrote:
> > On Wed, 2024-03-27 at 16:02 +0100, David Brown wrote:
> > > On 27/03/2024 14:32, wij wrote:
> > > > On Wed, 2024-03-27 at 13:57 +0100, Ralf Goertz wrote:
> > > > > Am Wed, 27 Mar 2024 20:12:38 +0800
> > > > > schrieb wij <wyniijj5@gmail.com>:
> > > > > 
> > > > > > On Wed, 2024-03-27 at 12:50 +0100, David Brown wrote:
> > > > > > > On 26/03/2024 22:43, wij wrote:
> > > > > > > > 
> > > > > > > > Just repeat the pattern infinitely, then it is irrational.
> > > > > > > 
> > > > > > > Nonsense.
> > > > > > >     
> > > > > > > > As said "∀x,a∈ℚ, x-a∈ℚ", if the subtraction a= 142857/10^(6*i)
> > > > > > > > cannot terminate, 1/7 != 0.(142857)
> > > > > > > >     
> > > > > > > 
> > > > > > > Nonsense.
> > > > > > >     
> > > > > > 
> > > > > > I am surprise your math. knowledge is so low worse than teenagers.
> > > > > 
> > > > > Use the standard trick:
> > > > > 
> > > > > x=0.[142857] => 1,000,000*x=142857.[142857]
> > > > > 
> > > > > subtract the first equation from the second:
> > > > > 
> > > > > 999,999*x=142857 => x=142857/999,999=1/7
> > > > > 
> > > > 
> > > > To determine whether a number x is rational or not, we can repeatedly subtract
> > > > rational numbers a? from x. If x-a1-a2-a3-...=0 can be verified in finite
> > > > steps, then x is rational. Otherwise, x is irrational.
> > > > If x is a repeating decimal, proposition "repeating decimal is rational" is
> > > > simply false by sematics.
> > > > 
> > > 
> > > Let me just ask you two simple questions:
> > > 
> > > Do you think 1/7 is a rational number or an irrational number?
> > > 
> > rational
> > 
> > > What do you think the decimal expansion of 1/7 is?
> > > 
> > 
> > When converting 1/7 to decimal, the result ≒ 0.(142857), the procedure
> > never terminates which means the conversion is never complete.
> > 
> 
> It is a repeating decimal.  If you try to write it all out, then I agree 
> you will not finish.  That does not mean it is not the decimal expansion 
> of 1/7 - the list of multiples of (negative) powers of 10 which sum up 
> to 1/7.  You just need a better notation so that you can finish the task 
> - and 0.(142857), as you wrote, is one such notation.
> 
> (I have no idea what you think the symbol "≒" might mean.)
> 
> But you agree that 0.(142857) is the decimal expansion of 1/7, even 
> though you could not write it out long-hand, and you agree that 1/7 i 
> rational.  And clearly 0.(142857) is a repeating decimal, since that's 
> what the notation means.
> 
> I can't see how you can still misunderstand this.
> 

You are restating your assertion without proof, again. I have provided mine.
(If you say that is you proof, I will say it is invalid).

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Thread

Repeating decimals are irrational wij <wyniijj5@gmail.com> - 2024-03-26 22:51 +0800
  Re: Repeating decimals are irrational Michael S <already5chosen@yahoo.com> - 2024-03-26 17:11 +0200
    Re: Repeating decimals are irrational Ben Bacarisse <ben.usenet@bsb.me.uk> - 2024-03-26 16:13 +0000
    Re: Repeating decimals are irrational Marcel Mueller <news.5.maazl@spamgourmet.org> - 2024-03-27 21:34 +0100
  Re: Repeating decimals are irrational "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-26 13:13 -0700
    Re: Repeating decimals are irrational wij <wyniijj5@gmail.com> - 2024-03-27 05:43 +0800
      Re: Repeating decimals are irrational David Brown <david.brown@hesbynett.no> - 2024-03-27 12:50 +0100
        Re: Repeating decimals are irrational wij <wyniijj5@gmail.com> - 2024-03-27 20:12 +0800
          Re: Repeating decimals are irrational Ralf Goertz <me@myprovider.invalid> - 2024-03-27 13:57 +0100
            Re: Repeating decimals are irrational wij <wyniijj5@gmail.com> - 2024-03-27 21:32 +0800
              Re: Repeating decimals are irrational wij <wyniijj5@gmail.com> - 2024-03-27 21:49 +0800
              Re: Repeating decimals are irrational David Brown <david.brown@hesbynett.no> - 2024-03-27 16:01 +0100
                Re: Repeating decimals are irrational "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-27 13:34 -0700
              Re: Repeating decimals are irrational David Brown <david.brown@hesbynett.no> - 2024-03-27 16:02 +0100
                Re: Repeating decimals are irrational wij <wyniijj5@gmail.com> - 2024-03-28 00:05 +0800
                Re: Repeating decimals are irrational "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-27 13:40 -0700
                Re: Repeating decimals are irrational wij <wyniijj5@gmail.com> - 2024-03-28 05:39 +0800
                Re: Repeating decimals are irrational "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-27 15:10 -0700
                Re: Repeating decimals are irrational "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-27 15:14 -0700
                Re: Repeating decimals are irrational David Brown <david.brown@hesbynett.no> - 2024-03-28 18:17 +0100
                Re: Repeating decimals are irrational wij <wyniijj5@gmail.com> - 2024-03-29 02:25 +0800
                Re: Repeating decimals are irrational David Brown <david.brown@hesbynett.no> - 2024-03-29 11:36 +0100
                Re: Repeating decimals are irrational David Brown <david.brown@hesbynett.no> - 2024-03-28 18:16 +0100
                Re: Repeating decimals are irrational wij <wyniijj5@gmail.com> - 2024-03-29 02:23 +0800
                Re: Repeating decimals are irrational David Brown <david.brown@hesbynett.no> - 2024-03-29 11:53 +0100
                Re: Repeating decimals are irrational wij <wyniijj5@gmail.com> - 2024-03-29 23:14 +0800
                Re: Repeating decimals are irrational David Brown <david.brown@hesbynett.no> - 2024-03-29 16:48 +0100
                Re: Repeating decimals are irrational wij <wyniijj5@gmail.com> - 2024-03-30 00:16 +0800
                Re: Repeating decimals are irrational "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-29 15:43 -0700
                Re: Repeating decimals are irrational David Brown <david.brown@hesbynett.no> - 2024-03-30 15:44 +0100
                Re: Repeating decimals are irrational "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-29 15:40 -0700
                Re: Repeating decimals are irrational Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2024-03-29 11:35 -0700
                Re: Repeating decimals are irrational David Brown <david.brown@hesbynett.no> - 2024-03-30 15:49 +0100
                Re: Repeating decimals are irrational wij <wyniijj5@gmail.com> - 2024-03-30 23:14 +0800
                Re: Repeating decimals are irrational David Brown <david.brown@hesbynett.no> - 2024-03-30 19:26 +0100
                Re: Repeating decimals are irrational wij <wyniijj5@gmail.com> - 2024-03-31 03:30 +0800
              Re: Repeating decimals are irrational "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-27 13:29 -0700
          Re: Repeating decimals are irrational David Brown <david.brown@hesbynett.no> - 2024-03-27 15:51 +0100
          Re: Repeating decimals are irrational "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-27 21:52 -0700
    Re: Repeating decimals are irrational Paavo Helde <eesnimi@osa.pri.ee> - 2024-03-26 23:51 +0200
      Re: Repeating decimals are irrational "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-26 19:42 -0700
        Re: Repeating decimals are irrational Paavo Helde <eesnimi@osa.pri.ee> - 2024-03-27 11:47 +0200
          Re: Repeating decimals are irrational David Brown <david.brown@hesbynett.no> - 2024-03-27 13:10 +0100
            Re: Repeating decimals are irrational "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-27 13:45 -0700
          Re: Repeating decimals are irrational Tim Rentsch <tr.17687@z991.linuxsc.com> - 2024-04-25 16:33 -0700
            Re: Repeating decimals are irrational David Brown <david.brown@hesbynett.no> - 2024-04-26 12:46 +0200
    Re: Repeating decimals are irrational David Brown <david.brown@hesbynett.no> - 2024-03-27 11:31 +0100
      Re: Repeating decimals are irrational "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-27 13:17 -0700
        Re: Repeating decimals are irrational David Brown <david.brown@hesbynett.no> - 2024-03-28 18:47 +0100
          Re: Repeating decimals are irrational "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-28 12:41 -0700
            Re: Repeating decimals are irrational David Brown <david.brown@hesbynett.no> - 2024-03-29 13:03 +0100
              Re: Repeating decimals are irrational "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-29 15:33 -0700
      Re: Repeating decimals are irrational "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-27 19:20 -0700
  Re: Repeating decimals are irrational usenet@stegropa.de (Stefan Große Pawig) - 2024-03-28 21:33 +0100
    Re: Repeating decimals are irrational wij <wyniijj5@gmail.com> - 2024-03-29 05:06 +0800

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