JT
Posts:
436
Registered:
4/7/12
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Re: 1/3 partitioned expansion in different bases
Posted:
Feb 2, 2013 1:07 AM
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On 2 Feb, 06:45, JT <jonas.thornv...@gmail.com> wrote:
> On 1 Feb, 15:06, Frederick Williams <freddywilli...@btinternet.com>
> wrote:
>
> > JT wrote:
> > > And 0.999... would be expressed as 0.3 or.......?
>
> > What are you asking? Does 0.9 recurring (in base 10) have the same
> > value as 0.3 (in base 3)? No, 0.9 recurring (in base 10) has the same
> > value as 1.0 (in base 3).
>
> > --
> > When a true genius appears in the world, you may know him by
> > this sign, that the dunces are all in confederacy against him.
> > Jonathan Swift: Thoughts on Various Subjects, Moral and Diverting
>
> Well actually in this numbersystem in base 3
> 0,3=1
> This means that 0,3 actually completes 0.999... in standard digit
> expansion, it is the sum of all possible fractions of a single natural
> number.
>
> So in my bases a single natural actually equals the sum of all
> fractions thus 1=0,3 in base 3 the decimal expansion is complete.
In reality though you will never use it since 3/3 equals one.
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