```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 isseparate the wholenumber part from the decimal part but of course ifthe number is 1111,1111 i could reencode it to 11111111 * (10^(-4)) =1111,1111 but then one must deal with the  base power.
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