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Groups > comp.lang.c++ > #118555
| From | Michael S <already5chosen@yahoo.com> |
|---|---|
| Newsgroups | comp.lang.c++ |
| Subject | Re: Repeating decimals are irrational |
| Date | 2024-03-26 17:11 +0200 |
| Organization | A noiseless patient Spider |
| Message-ID | <20240326181126.00004b3c@yahoo.com> (permalink) |
| References | <5b363d215e2c4dab1d496efee2655409dcecf655.camel@gmail.com> |
On Tue, 26 Mar 2024 22:51:40 +0800
wij <wyniijj5@gmail.com> wrote:
> 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
>
I don't know what you meant to say, but repeating (a.k.a. periodic)
decimals are most certainly rational numbers. I think that proving it
would be rather easy although I didn't try to do it in rigorous
manner. The idea of proof is multiplying repeating decimal with period P
by (10**P-1) will produce finite decimal. Which is obviously rational.
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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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