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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:
1,306
Registered:
4/7/12


Re: Is there any webpage or math program that can write fracitons, numbers into bijective enumeration?
Posted:
Mar 23, 2013 7:32 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.
We could also just take the decimal part ,1111 and raise the power to a natural 0,1111 * (10^4)



