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}

>

> 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.