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:
Apr 2, 2013 7:51 AM


On 2 Apr, 13:10, JT <jonas.thornv...@gmail.com> wrote: > On 2 Apr, 13:05, JT <jonas.thornv...@gmail.com> wrote: > > > > > > > > > > > On 2 Apr, 12:59, JT <jonas.thornv...@gmail.com> wrote: > > > > On 31 mar, 23:11, 1treePetrifiedForestLane <Space...@hotmail.com> > > > wrote: > > > > > just pick a number, like "five," > > > > and represent it in each of the bases, from ten, down to > > > > the last possible "natural" digital representation, > > > > to see how it cameabout, in the first place. > > > > Bases of the naturals is due to partitioning of discrete entities, as > > > collections or sets if you so want, as you can understand the number > > > of embrasing parentheses signifies grouping and digit position it is > > > all very *basic*. > > > > Counting 5={1,1,1,1,1} > > > Binary 5={{1,1}{1,1}1} > > > Ternary 5={{1,1,1}1,1} > > > Quaternary 5={{1,1,1,1}1} > > > Senary 5={1,1,1,1,1} > > > Septenary 5={1,1,1,1,1} > > > Octal 5={1,1,1,1,1} > > > Nonary 5={1,1,1,1,1} > > > Decimal 5={1,1,1,1,1} > > > As you can see each digit position contain groups of the base. This is > > what numbers and the partitioning of the naturals really is about, the > > numberline is just a figment due to introduction of measuring, but > > numbers at base 1, the collection created by counting do not have > > geometric properties until you start partition the collection into a > > base. > > A number as expressed using a base is a geometric perspective upon a > collecton of discrete entities. So depending upon if you use a > zeroless or a standard base the geometric properties change of the > collection. This is closely related to factoring.
What is interesting but elementary when writing out a number into a base is to notice that every second digit plase is a square. Digit place ternary 1 3 2 9 square 3 3 27 4 81 square 9 5 243 6 729 square 27 7 2187 8 6561 square 81
And this is the geometric properties of numbers lines building up squares, when you use zero in a base this you mash up all minor squares into a bigger. 70000000000000000000000000000000000700000000000000000000000000000000000000000000000000900000000000000000000000000000000000000000000000000000000003 is it prime? So the geometric properties using Nyan is totally different since each full base render a smaller square so the numbers become a sum of squares and their lines.

