Date: Mar 22, 2013 11:20 AM
Author: JT
Subject: Re: Is there any webpage or math program that can write fracitons,<br> numbers into bijective enumeration?

On 19 mar, 09:36, JT <jonas.thornv...@gmail.com> wrote:
> On 19 mar, 07:18, JT <jonas.thornv...@gmail.com> wrote:
>

> > Surely someone must found it interesting enough to implement it?
> > A generic basechanger working in anybase for bijective encoded numbers
> > would be nice.

>
> Could anyone gifted? mathematician help me encode the positive numbers
> upon the following bijective (NyaN) form?
>
> Binary      1=.2   1/2=.1  2/2=.2   1/4=.(1)1    2/4=.(1)2
> Ternary     1=.3   1/3=.1  2/3=.2   1/9=.(1)1    2/9=.(1)2  1/27=.
> (2)1    2/27=.(2)2   1/81=.(3)1   2/81=.(3)2
> Quaternary  1=.4   1/4=.1  2/4=.2   1/16=.(1)1   2/16=.(1)2
> Quinary     1=.5   1/5=.1  2/5=.2   1/25=.(1)1   2/25=.(1)2
> Senary      1=.6   1/6=.1  2/6=.2   1/36=.(1)1   2/36=.(1)2
> Septenary   1=.7   1/7=.1  2/7=.2   1/49=.(1)1   2/49=.(1)2
> Octal       1=.8   1/8=.1  2/8=.2   1/64=.(1)1   2/64=.(1)2
> Nonary      1=.9   1/9=.1  2/9=.2   1/81=.(1)1   2/81=.(1)2
> Decimal     1=.A   1/10=.1 2/10=.2  1/100=.(1)1  2/100=.(1)2
>
> Ternary maybe the best choice for checking out the results of your
> generic recursive base implementation since it fairly easy to follow
> what is goin on.
> 1/3       = .1
> 2/3       = .2
> 1/9       = .(1)1
> 2/9       = .(1)2
> 1/27      = .(2)1
> 2/27      = .(2)2
> 1/81      = .(3)1
> 2/81      = .(3)2
>
> And for the Naturals
> 1   =1
> 2   =2
> 3   =3
> 4   =11 3+1
> 5   =12 3+2
> 6   =13 3+3
> 7   =21 6+1
> 8   =22 6+2
> 9   =23 6+3
> 10  =31 9+1
> 11  =32 9+2
> 12  =33 9+3
> 13  =111 9+3+1
> 14  =112 9+3+2
> 15  =113 9+3+3
> 16  =121 9+6+1
> 17  =122 9+6+2
> 18  =123 9+6+3
> 19  =131 9+9+1
> 20  =132 9+9+2
> 21  =133 9+9+3
>
> Here is a start for your attempt to make an algorithm that will encode
> any decimal number with decimal parts into anybase,(i can't quite get
> it right but for you guys it should be pieceof a cake).
> It is maximum two lines of code.http://www.anybase.co.nf/


Regarding changing bases of reals like i do in script above, there is
separate the wholenumber part from the decimal part but of course if
the number is 1111,1111 i could reencode it to 11111111 * (10^(-4)) =
1111,1111 but then one must deal with the base power.