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Topic: Can a fraction have none noneending and nonerepeating decimal representation?
Replies: 108   Last Post: Aug 16, 2013 5:22 PM

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magidin@math.berkeley.edu

Posts: 11,162
Registered: 12/4/04
Re: Can a fraction have none noneending and nonerepeating decimal representation?
Posted: Aug 1, 2013 12:09 PM
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On Wednesday, July 31, 2013 4:46:04 PM UTC-5, jonas.t...@gmail.com wrote:
> Den onsdagen den 31:e juli 2013 kl. 23:29:08 UTC+2 skrev Virgil:
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> > In article <b9e8c466-494c-4588-a1fb-7bc158632e2a@googlegroups.com>,
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> > jonas.thornvall@gmail.com wrote:
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> > > Den onsdagen den 31:e juli 2013 kl. 22:22:28 UTC+2 skrev Virgil:
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> > > > In article <396e3715-0ca7-4dcf-8962-29fa30a5eda8@googlegroups.com>,
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> > > > > Den tisdagen den 30:e juli 2013 kl. 21:39:04 UTC+2 skrev Virgil:
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> > > > > > In article <3ef71a1a-0168-4f56-bc9e-f4af3d5f9fe0@googlegroups.com>,
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> > > > > > jonas.thornvall@gmail.com wrote:
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> > > > > > > Den tisdagen den 30:e juli 2013 kl. 17:12:38 UTC+2 skrev
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> > > > > > > jonas.t...@gmail.com:
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> > > > > > > > Can a fraction have none noneending and nonerepeating decimal
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> > > > > > > I was thinking that is seem that the choice of base to represent
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> > > > > > > can lead to nonending repetive patterns, but can they also be none
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> > > > > > In any natural number base, not only base ten decimals, rationals are
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> > > > > > > I guess not, but a rounding error calculating Pi could easily
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> > > > > > > perfectly rational fraction to irrational, isn't that true?
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> > > > > > > A *SLIGHT* flaw in the arithmetic
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> > > > > Well what i said was that a slight error doing arithmetics could prevent
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> > > > A rounding error in calculating pi is much more likely to make pi seem
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> > > > rational, since in calculating pi without error it is not.
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> > > Or your arithmetic is not upto it, who knows
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> > Those who know pi is irrational all know!
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> Yes Pi is considered to be irrational until proven differently,


No. Pi is *demonstrably* not only irrational, but in fact transcendental. It's not something that is "considered until proven differently", it's something that has *already been proven*.

> using another base, maybe a bijective base or written out as fraction.

Rationality is base-independent. That is, as has been explained repeatedly: whether a number is rational or irrational does not depend on the base that one uses to *represent* the number.

Whether the base-n representation of a RATIONAL number *terminates* or not *does* depend on the value of n: in general, a fraction a/b written in lowest terms has a terminating base-n representation if and only if there is a power of n that is a multiple of b; thus, in decimal notation, the only fractions with terminating base-10 representation are those which, when written in lowest terms, have a denominator of the form 2^r*5^s, with r and s positive integers.

I have no idea what "bijective base" is supposed to mean. But do not confuse properties of the *representation* of a number with properties of the *number*. The quantity of symbols needed to represent a number may depend on the base or on the language being used. But whether the number is rational or not is a property of the number, not of its representation.

--
Arturo Magidin


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> I hope you do also realise that 1/3 have none terminating decimal expansion in decimal base. But have no problem terminating in bijective base 3.




Date Subject Author
7/30/13
Read Can a fraction have none noneending and nonerepeating decimal representation?
JT
7/30/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
7/30/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Virgil
7/31/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
7/31/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Virgil
7/31/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
7/31/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Tucsondrew@me.com
7/31/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
7/31/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Tucsondrew@me.com
7/31/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
7/31/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Tucsondrew@me.com
7/31/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
7/31/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Virgil
7/31/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Virgil
7/31/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
7/31/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Tucsondrew@me.com
7/31/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
7/31/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Tucsondrew@me.com
7/31/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
7/31/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
7/31/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
7/31/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
7/31/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
7/31/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
LudovicoVan
7/31/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
7/31/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
LudovicoVan
7/31/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
7/31/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
7/31/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
7/31/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Virgil
8/1/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
8/1/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
8/1/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Virgil
8/1/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Virgil
8/1/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
8/1/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Virgil
8/1/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Virgil
8/3/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
grei
7/31/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
8/4/13
Read the surfer's value (Nicholas de Cusa proved that pi was
transcendental in the 15th cue (http://21stcenturysciencetech.com
Brian Q. Hutchings
8/4/13
Read Re: the surfer's value (Nicholas de Cusa proved that pi was
transcendental in the 15th cue (http://21stcenturysciencetech.com
Brian Q. Hutchings
7/31/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Tucsondrew@me.com
7/31/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation? NO!
Virgil
8/1/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
magidin@math.berkeley.edu
8/1/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
8/1/13
Read Re: Can a fraction have none noneending and nonerepeating decimal
representation?
Peter Percival
8/1/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
8/1/13
Read Re: Can a fraction have none noneending and nonerepeating decimal
representation?
Peter Percival
8/1/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
8/1/13
Read Re: Can a fraction have none noneending and nonerepeating decimal
representation?
Peter Percival
8/1/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
8/1/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Virgil
8/1/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Virgil
8/1/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Virgil
8/1/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Virgil
8/1/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
magidin@math.berkeley.edu
8/1/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
8/1/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
8/1/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Virgil
8/1/13
Read Re: Can a fraction have none noneending and nonerepeating decimal
representation?
Peter Percival
8/1/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
8/1/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Virgil
8/1/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
8/1/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Virgil
8/1/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Virgil
8/1/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
magidin@math.berkeley.edu
8/1/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Richard Tobin
8/2/13
Read Re: Can a fraction have none noneending and nonerepeating decimal
representation?
David Bernier
8/2/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
8/2/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Richard Tobin
8/2/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
8/2/13
Read Re: Can a fraction have none noneending and nonerepeating decimal
representation?
Peter Percival
8/2/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Richard Tobin
8/2/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
8/2/13
Read Re: Can a fraction have none noneending and nonerepeating decimal
representation?
Peter Percival
8/2/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Richard Tobin
8/16/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Earle Jones
8/2/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Virgil
8/2/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
8/2/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
RGVickson@shaw.ca
8/2/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
8/2/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Virgil
8/2/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
8/2/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Virgil
8/2/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Virgil
8/2/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Virgil
8/2/13
Read Re: Can a fraction have none noneending and nonerepeating decimal
representation?
David Bernier
8/2/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
8/2/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Virgil
8/2/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
8/2/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
8/2/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Virgil
8/3/13
Read Re: Can a fraction have none noneending and nonerepeating decimal
representation?
David Bernier
8/3/13
Read Re: Can a fraction have none noneending and nonerepeating decimal
representation?
David Bernier
8/4/13
Read Re: Can a fraction have none noneending and nonerepeating decimal
representation?
David Bernier
8/2/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
quasi
8/2/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
8/2/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
8/2/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Virgil
8/2/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Shmuel (Seymour J.) Metz
8/2/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
8/2/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Virgil
8/2/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
FredJeffries@gmail.com
8/16/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Earle Jones
7/31/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
7/31/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Phil H
7/31/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
7/30/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Earle Jones

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