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Re: Why not Hausdorff's ordered pairs
Posted:
Feb 22, 2012 7:16 PM
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On Tue, 21 Feb 2012 07:48:03 -0500, Shmuel Metz
<spamtrap@library.lspace.org.invalid> said:
> In <slrnjk71dv.put.cmenzel@philebus.tamu.edu>, on 02/21/2012
> at 11:53 AM, Chris Menzel <cmenzel@remove-this.tamu.edu> said:
>
>>Judgments differ regarding naturalness but one issue is that K's
>>definition of <a,b> does not involve objects other than a and b (and
>>sets immediately constructed from them) in the definition. I myself
>>find that a bit more "natural" than pulling two arbitrarily chosen
>>objects into the definition that (in general) have no connection
>>whatever to a and b.
>
> While I find (a,b)={{a},{a,b}} to be more natural for ordered pairs,
> it does not generalize well to m-tuples.
But only in regard to "naturalness", right? I mean, in general, for
n>1, we have <a1,...,an,an+1> = <<a1,...,an>,an+1> = {{<a1,...,an>},
{<a1,...,an>},{an+1}}, which is perfectly well defined under K's
definition.
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