Date: Mar 25, 2013 3:54 AM
Author: JT
Subject: Re: Is there any webpage or math program that can write fracitons,<br> numbers into bijective enumeration?

On 25 mar, 08:48, JT <jonas.thornv...@gmail.com> wrote:
> On 25 mar, 04:51, david petry <david_lawrence_pe...@yahoo.com> wrote:
>

> > On Thursday, March 21, 2013 2:52:56 AM UTC-7, JT wrote>
>
> > Ternary NyaN format
>
> > > 1=1        {1}
>
> > > 2=2        {1,1}
>
> > > 3=3        {1,1,1}
>
> > If I search for "NyaN" in Google, I get links to some YouTube cat video.  If I search for "Nyan fractions" I get links to your article.
>
> > So what does "NyaN" mean?
>
> Ny or nya means new in swedish and N is the  positive integers, the
> NyaN algorithm encode the positive integers into a a bijective?
> zeroless basesystems (anybase). I constructed the algorithm that can
> convert any positive real into NyaN format, see below.
>
> 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


The NyaN cat just roaming all over the numberline, it is in the music
so there is no wall of infinity, no steps due to zeros and no abyss.
Just countable numbers.