```Date: Mar 22, 2013 11:23 AM
Author: JT
Subject: Re: Is there any webpage or math program that can write fracitons,<br> numbers into bijective enumeration?

On 22 mar, 16:20, JT <jonas.thornv...@gmail.com> wrote:> 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.And then the base changing function would work for any real, (it isright now too) but maybe not that aestethical from  a math perspective?
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