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Topic: Is there any webpage or math program that can write fracitons,
numbers into bijective enumeration?

Replies: 68   Last Post: Apr 8, 2013 11:40 PM

 Messages: [ Previous | Next ]
 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 7:51 AM

On 2 Apr, 13:10, JT <jonas.thornv...@gmail.com> wrote:
> On 2 Apr, 13:05, JT <jonas.thornv...@gmail.com> wrote:
>
>
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>

> > 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.

>
> 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.

What is interesting but elementary when writing out a number into a
base is to notice that every second digit plase is a square.
Digit place ternary
1 3
2 9 square 3
3 27
4 81 square 9
5 243
6 729 square 27
7 2187
8 6561 square 81

And this is the geometric properties of numbers lines building up
squares, when you use zero in a base this you mash up all minor
squares into a bigger.
70000000000000000000000000000000000700000000000000000000000000000000000000000000000000900000000000000000000000000000000000000000000000000000000003
is it prime?
So the geometric properties using Nyan is totally different since each
full base render a smaller square so the numbers become a sum of
squares and their lines.

Date Subject Author
3/19/13 JT
3/19/13 JT
3/20/13 JT
3/20/13 Robin Chapman
3/20/13 Brian Q. Hutchings
3/20/13 JT
3/20/13 JT
3/20/13 JT
3/20/13 JT
3/20/13 Brian Q. Hutchings
3/20/13 JT
3/20/13 Brian Q. Hutchings
3/21/13 JT
3/23/13 Brian Q. Hutchings
3/24/13 JT
3/21/13 JT
3/21/13 JT
3/24/13 David Petry
3/25/13 JT
3/25/13 JT
3/25/13 JT
3/26/13 JT
3/28/13 JT
3/31/13 Brian Q. Hutchings
4/2/13 JT
4/2/13 JT
4/2/13 JT
4/2/13 JT
4/2/13 JT
4/2/13 JT
4/4/13 JT
4/6/13 KBH
4/6/13 JT
4/6/13 JT
4/6/13 JT
4/6/13 JT
4/5/13 Brian Q. Hutchings
4/6/13 JT
4/6/13 JT
4/6/13 JT
3/20/13 JT
3/22/13 JT
3/22/13 JT
3/23/13 JT
3/23/13 JT
3/23/13 JT
3/23/13 JT
3/26/13 JT
3/31/13 JT
3/31/13 Brian Q. Hutchings
4/7/13 KBH
4/7/13 KBH
4/7/13 KBH
4/7/13 KBH
4/7/13 JT
4/7/13 JT
4/7/13 KBH
4/7/13 JT
4/7/13 JT
4/7/13 JT
4/8/13 Brian Q. Hutchings
4/7/13 KBH
4/7/13 JT
4/8/13 Brian Q. Hutchings
4/7/13 JT
3/31/13 Frederick Williams
3/31/13 JT
4/7/13