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Topic: Why not Hausdorff's ordered pairs
Replies: 70   Last Post: Feb 25, 2012 3:01 AM

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 Graham Cooper Posts: 4,124 Registered: 5/20/10
Re: Why not Hausdorff's ordered pairs
Posted: Feb 24, 2012 2:46 PM

On Feb 24, 10:25 pm, Zuhair <zaljo...@gmail.com> wrote:
> On Feb 24, 2:34 pm, Graham Cooper <grahamcoop...@gmail.com> wrote:
>
>
>

> > you added the braces around {a} {b} {c} for a reason, so you could
> > determine the {position,{data}} order.

>
> EXACTLY! what I see it nice about it is how it simplifies sequences
> so for example a sequnce S= 7,63, 2
>
> Instead of implementing this as S= { {{1},{1,7}} , {{2},{2,63}} , {{3},
> {3,2}} }
> which is the customary way using Kuratowski pairs based sequence.
> We can simplify that to S= { {1,{7}} , {2,{63}} , {3,{2}} } which is
> much
> simpler really.

Not in sets it isn't!

Instead of a duplicate redundancy on the numerical index n,
you repeat it n times.

To remove the duplicate index, you have to slice the index into an n
elements set.

{ {3},{3,C} } K Pair
VS
{ {2, 1, 0}, {C} } Z Pair

K Pairs use SET SUBSTRACTION to identifiy the first ordinate/index
Your system uses SET.SIZE>1 member sets to identify the index

Note in K Pair, Naturals can be represented O(n) {{{{{}}}}}

where Von Neuman Numbers are size & time expensive O(n^2) for no
reason.

Breaking your 3rd Ordinate down further..

{ { { {} {{}} }, {{}}, {} }, {C} }

VS K Pairs
{ { {{{}}} }, { {{{}}}, C} }

You are forced to construct arbitrary DISTINCT SETS
in order to count them to represent the Natural by it's SET SIZE =
MEMBER COUNT

{ DIFFERENT, DIFFERENT, DIFFERENT, DIFFERENT } = 4

In pure sets, this is 4 levels of recursion O(n^2) data structure.

You couldn't represent a million digits of Pi on a modern computer in

Herc
--
http://Matheology.com

Date Subject Author
2/20/12 Zaljohar@gmail.com
2/20/12 Kaba
2/20/12 Herman Rubin
2/20/12 Zaljohar@gmail.com
2/20/12 David Yen
2/21/12 Chris Menzel
2/21/12 Shmuel (Seymour J.) Metz
2/21/12 Zaljohar@gmail.com
2/21/12 Zaljohar@gmail.com
2/21/12 namducnguyen
2/21/12 Shmuel (Seymour J.) Metz
2/21/12 namducnguyen
2/21/12 namducnguyen
2/22/12 Shmuel (Seymour J.) Metz
2/22/12 namducnguyen
2/22/12 Shmuel (Seymour J.) Metz
2/22/12 Zaljohar@gmail.com
2/22/12 Herman Rubin
2/22/12 Zaljohar@gmail.com
2/22/12 Graham Cooper
2/22/12 Graham Cooper
2/22/12 Graham Cooper
2/22/12 Chris Menzel
2/22/12 Graham Cooper
2/23/12 Graham Cooper
2/23/12 Herman Rubin
2/23/12 Graham Cooper
2/23/12 Zaljohar@gmail.com
2/23/12 Zaljohar@gmail.com
2/23/12 Zaljohar@gmail.com
2/23/12 Graham Cooper
2/23/12 Zaljohar@gmail.com
2/23/12 Zaljohar@gmail.com
2/23/12 Zaljohar@gmail.com
2/23/12 Herman Rubin
2/23/12 Graham Cooper
2/23/12 Zaljohar@gmail.com
2/23/12 Graham Cooper
2/23/12 Zaljohar@gmail.com
2/23/12 Graham Cooper
2/23/12 Graham Cooper
2/24/12 Zaljohar@gmail.com
2/24/12 Graham Cooper
2/24/12 Zaljohar@gmail.com
2/24/12 Zaljohar@gmail.com
2/24/12 Graham Cooper
2/24/12 Zaljohar@gmail.com
2/24/12 Zaljohar@gmail.com
2/24/12 Zaljohar@gmail.com
2/24/12 Graham Cooper
2/24/12 Zaljohar@gmail.com
2/24/12 Graham Cooper
2/24/12 Zaljohar@gmail.com
2/24/12 Graham Cooper
2/24/12 Graham Cooper
2/24/12 Zaljohar@gmail.com
2/24/12 Graham Cooper
2/25/12 Zaljohar@gmail.com
2/25/12 Graham Cooper
2/23/12 Zaljohar@gmail.com
2/23/12 Graham Cooper
2/23/12 Zaljohar@gmail.com
2/23/12 Zaljohar@gmail.com
2/23/12 Graham Cooper
2/23/12 Zaljohar@gmail.com
2/23/12 Graham Cooper
2/23/12 Zaljohar@gmail.com
2/23/12 Shmuel (Seymour J.) Metz
2/21/12 Zaljohar@gmail.com
2/22/12 Zaljohar@gmail.com
2/22/12 Graham Cooper