Date: Apr 2, 2013 7:10 AM
Author: JT
Subject: Re: Is there any webpage or math program that can write fracitons,<br> numbers into bijective enumeration?

On 2 Apr, 13:05, JT <jonas.thornv...@gmail.com> wrote:
> On 2 Apr, 12:59, JT <jonas.thornv...@gmail.com> wrote:
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> > On 31 mar, 23:11, 1treePetrifiedForestLane <Space...@hotmail.com>
> > wrote:

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> > > 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.

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> > 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*.

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> > 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}

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> 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.