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.