Date: Apr 2, 2013 7:05 AM
Author: JT
Subject: Re: Is there any webpage or math program that can write fracitons,<br> numbers into bijective enumeration?
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 came-about, 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.