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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



JT
Posts:
1,343
Registered:
4/7/12


Re: Is there any webpage or math program that can write fracitons, numbers into bijective enumeration?
Posted:
Mar 22, 2013 11:23 AM


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 is right now too) but maybe not that aestethical from a math perspective?



