Re: Repeating decimals are irrational

From	David Brown <david.brown@hesbynett.no>
Newsgroups	comp.lang.c++
Subject	Re: Repeating decimals are irrational
Date	2024-03-28 18:17 +0100
Organization	A noiseless patient Spider
Message-ID	<uu48o7$3n14g$2@dont-email.me> (permalink)
References	(6 earlier) <c256dbb376440ca8535bb27a0ecebb37304a583f.camel@gmail.com> <uu1cel$2te2i$2@dont-email.me> <435b9fe3357bbc4dd5a25f8f9e75637e270dd55b.camel@gmail.com> <uu208r$31us4$4@dont-email.me> <b6d1e08e83e5bf171adec0cc0c065d62c3c695b4.camel@gmail.com>

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On 27/03/2024 22:39, wij wrote:
> On Wed, 2024-03-27 at 13:40 -0700, Chris M. Thomasson wrote:
>> On 3/27/2024 9:05 AM, 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.
>>>
>>>
>>>
>>
>> You can stop iteration as soon as you detect a cycle, or period if you
>> will. In 1/7, say it took 6 iterations to hit the period... Sound okay?
> 
> Stupid! It is an infinite string. Cycle or period can only be determined for
> finite string.
> 

Nonsense.

You /know/ the cycle for the infinite decimal expansion for 1/7 - it is 
the digits "142857", repeated every 6 digits in the decimal expansion. 
Again, that's what the notation 0.(142857) - /your/ choice of notation, 
so presumably familiar to you - means.

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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