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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:
1,448
Registered:
4/7/12


Re: Is there any webpage or math program that can write fracitons, numbers into bijective enumeration?
Posted:
Mar 19, 2013 4:36 AM


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/



