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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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 Zaljohar@gmail.com Posts: 2,632 Registered: 6/29/07
Re: Why not Hausdorff's ordered pairs
Posted: Feb 21, 2012 3:52 PM

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.
>

Well this definition also doesn't generalize well to m-tuples. A
definition that might generalize to m-tuples
is to define them as sequences so
(a_1,...,a_m)={<{},a_1>,<{{}},a_2>,<{{},{{}}},a_3>,..., <m_th
ordinal,a_m>}
where <> is defined after the definition above. Actually we can even
produce an infinite tuple this way.

Zuhair

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2/23/12 Zaljohar@gmail.com
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2/24/12 Zaljohar@gmail.com
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2/23/12 Graham Cooper
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2/23/12 Shmuel (Seymour J.) Metz
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2/22/12 Graham Cooper