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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: 1,434 Registered: 4/7/12
Re: Is there any webpage or math program that can write fracitons,
numbers into bijective enumeration?

Posted: Mar 25, 2013 3:48 AM

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

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
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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
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3/25/13 JT
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3/31/13 Brian Q. Hutchings
4/2/13 JT
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4/6/13 KBH
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4/5/13 Brian Q. Hutchings
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3/31/13 JT
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4/7/13 KBH
4/7/13 KBH
4/7/13 KBH
4/7/13 KBH
4/7/13 JT
4/7/13 JT
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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