Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
NCTM or The Math Forum.


Math Forum
»
Discussions
»
sci.math.*
»
sci.math
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



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 3:54 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 UTC7, 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.



