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List:       python-list
Subject:    Re: Would there be support for a more general cmp/__cmp__
From:       "Steven D'Aprano" <steve () REMOVETHIScyber ! com ! au>
Date:       2005-10-25 14:50:12
Message-ID: pan.2005.10.25.14.50.12.136272 () REMOVETHIScyber ! com ! au
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On Tue, 25 Oct 2005 10:09:29 -0400, Christopher Subich wrote:

>>>By analogy, one can ask, "is the cat inside the box?" and get the answer
>>>"No", but this does not imply that therefore the box must be inside the
>>>cat.
>> 
>> 
>> Bad analogy, this doesn't define a mathematical ordering, the subset
>> relationship does.
> 
> Yes, it does.  Consider "in" as a mathematical operator:
>
> For the set (box, cat-in-box)
> 
> box in box: False
> box in cat-in-box: False
> cat-in-box in box: True
> cat-in-box in cat-in-box: False
> 
> For the set (box, smart-cat) # cat's too smart to get in the box
> 
> box in box: False
> box in smart-cat: False
> smart-cat in box: False
> smart-cat in smart-cat: False
> 
> In both these cases, the "in" operator is irreflexive, asymmetric, and 
> transitive (extend to mouse-in-cat if you really care about transitive), 
> so "in" is a partial order sans equality.  A useless one, but a partial 
> order nonetheless.

What do you mean "in" is a useless ordering? It makes a huge difference
whether "nuclear bomb in New York" is true or not.

In fact, I'm quite surprised that Antoon should object to "in" as "this
doesn't define a mathematical ordering, the subset relationship does" when
"subset" is just "in" for sets: set S is a subset of set T if for all
elements x in S, x is also in T. Informally, subset S is in set T.

Can somebody remind me, what is the problem Antoon is trying to solve here?


-- 
Steven.

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