Re: Repeating decimals are irrational

From	wij <wyniijj5@gmail.com>
Newsgroups	comp.lang.c++
Subject	Re: Repeating decimals are irrational
Date	2024-03-29 05:06 +0800
Organization	A noiseless patient Spider
Message-ID	<47650025b29f69050d08fbdf0ce898d40bbb9b07.camel@gmail.com> (permalink)
References	<5b363d215e2c4dab1d496efee2655409dcecf655.camel@gmail.com> <87jzlmhzad.fsf@ID-208667.user.individual.de>

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On Thu, 2024-03-28 at 21:33 +0100, Stefan Große Pawig wrote:
> wij <wyniijj5@gmail.com> writes:
> > Snipet from https://sourceforge.net/projects/cscall/files/MisFiles/RealNumber-en.txt/download
> > 
> > ...
> > Real Nunmber(ℝ)::= {x| x is represented by n-ary <fixed_point_number>, the
> >    digits may be infinitely long }
> > 
> >    Note: This definition implies that repeating decimals are irrational number.
> >          Let's list a common magic proof in the way as a brief explanation:
> >            (1) x= 0.999...
> >            (2) 10x= 9+x  // 10x= 9.999...
> >            (3) 9x=9    
> >            (4) x=1
> >          Ans: There is no axiom or theorem to prove (1) => (2).
> > 
> >    Note: If the steps of converting a number x to <fixed_point_number> is not
> >          finite, x is not a ratio of two integers, because the following
> >          statement is always true: ∀x,a∈ℚ, x-a∈ℚ
> > 
> > ---End of quote
> 
> What does the arity of the "n-ary <fixed_point_number>" refer to? The
> base or the number of digits?
> 

Yes, base of the number system.

> Any rational number can be represented with a single fractional digit
> when represented in the base of its denominator.
> 
> I.e., 3/7 = 0.3 (base 7)
> 
> And as far as I am aware, the rationality of a number does not depend on
> its representation...
> 

Exactly.

You quoted a slightly outdated text. Click the link above to see the most updated text.

> -Stefan
>

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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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