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

 Messages: [ Previous | Next ]
 Graham Cooper Posts: 4,495 Registered: 5/20/10
Re: Why not Hausdorff's ordered pairs
Posted: Feb 22, 2012 2:40 PM

On Feb 23, 4:12 am, Zuhair <zaljo...@gmail.com> wrote:
> On Feb 21, 3:48 pm, Shmuel (Seymour J.) Metz
>
> <spamt...@library.lspace.org.invalid> wrote:

> > In <slrnjk71dv.put.cmen...@philebus.tamu.edu>, on 02/21/2012
> >    at 11:53 AM, Chris Menzel <cmen...@remove-this.tamu.edu> said:

>
> > While I find (a,b)={{a},{a,b}} to be more natural for ordered pairs,
> > it does not generalize well to m-tuples.

>
> Actually Hausdorff's generalize much much better than Kuratowski's.
> Compare between
>  (a,b,c)={{1,a},{{2,b},{3,c}}}  and (a,b,c)={{a},{a,{{b},{b,c}}}}
> which is very Ugly. The nice thing is that Haudorff's admits simple
> tagging of projections according to their order, and this is the
> secret of its naturally looking strength.
>
> Zuhair

Who on Earth has ever practically used the syntax

{{1,a},{{2,b},{3,c}}}

It's a miss match of notation.

Just use (a, b, c)

It doesn't even work!

{ {3,2} , {2,1} , {1,3} }

= { {2,3} , {1,2} , {3,1} }

{{1,a},{2,b}}={{1,c},{2,d}} entails [{1,a}={1,c} & {2,b}={2,d}]
thus
a=c & b=d
or [{1,a}={2,d} & {2,b}={1,c}] thus a=2,d=1,b=1,c=2 thus a=c & b=d.
QED

How are you defining NUMBERS without ORDERED PAIRS?

You can't even write down EQUALS( S(a), a+1 )

It's like saying - HEY LETS USE NEUTRINOS TO COUNT CALORIES INSTEAD!

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