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 7:10 AM


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.

