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Topic: Is there any webpage or math program that can write fracitons,
numbers into bijective enumeration?

Replies: 68   Last Post: Apr 8, 2013 11:40 PM

 Messages: [ Previous | Next ]
 JT Posts: 1,448 Registered: 4/7/12
Re: Is there any webpage or math program that can write fracitons,
numbers into bijective enumeration?

Posted: Mar 25, 2013 3:58 AM

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

And in a broader sense NyaN cat is a reference to the futilities of
infinities, and events and arguments going on for more then decades.

Date Subject Author
3/19/13 JT
3/19/13 JT
3/20/13 JT
3/20/13 Robin Chapman
3/20/13 Brian Q. Hutchings
3/20/13 JT
3/20/13 JT
3/20/13 JT
3/20/13 JT
3/20/13 Brian Q. Hutchings
3/20/13 JT
3/20/13 Brian Q. Hutchings
3/21/13 JT
3/23/13 Brian Q. Hutchings
3/24/13 JT
3/21/13 JT
3/21/13 JT
3/24/13 David Petry
3/25/13 JT
3/25/13 JT
3/25/13 JT
3/26/13 JT
3/28/13 JT
3/31/13 Brian Q. Hutchings
4/2/13 JT
4/2/13 JT
4/2/13 JT
4/2/13 JT
4/2/13 JT
4/2/13 JT
4/4/13 JT
4/6/13 KBH
4/6/13 JT
4/6/13 JT
4/6/13 JT
4/6/13 JT
4/5/13 Brian Q. Hutchings
4/6/13 JT
4/6/13 JT
4/6/13 JT
3/20/13 JT
3/22/13 JT
3/22/13 JT
3/23/13 JT
3/23/13 JT
3/23/13 JT
3/23/13 JT
3/26/13 JT
3/31/13 JT
3/31/13 Brian Q. Hutchings
4/7/13 KBH
4/7/13 KBH
4/7/13 KBH
4/7/13 KBH
4/7/13 JT
4/7/13 JT
4/7/13 KBH
4/7/13 JT
4/7/13 JT
4/7/13 JT
4/8/13 Brian Q. Hutchings
4/7/13 KBH
4/7/13 JT
4/8/13 Brian Q. Hutchings
4/7/13 JT
3/31/13 Frederick Williams
3/31/13 JT
4/7/13