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Re: singleton sets

From: Ian Emmons <iemmons@bbn.com>
Date: Tue, 12 Aug 2008 19:23:15 -0400
Message-Id: <34E055C1-B031-4ACF-8EB1-90DADE2F0480@bbn.com>
To: Semantic Web at W3C <semantic-web@w3.org>

On Aug 12, 2008, at 6:39 PM, Michael Schneider wrote:

 >> Even if x is a set, we must not confuse it with its own singleton.
 >> For example, x might have any number of elements in it, but {x} has
 >> exactly one element: x.
 > Wait, now I'm confused! How can there be a singleton for the *set* x?
 > Isn't it crazy to talk about sets, which are themselves included in  

I'm not sure if such situations are relevant for the Semantic Web, but  
mathematicians talk about such things all the time.  For instance,  
given a set S, it is often interesting to talk about the set of all  
continuous functions from S to S.  (I am, of course, assuming that S  
has enough structure so that the notion of "continuous" is well- 
defined.)  But a function from S to S is merely a subset of SxS (the  
Cartesian product of S with itself) that obeys certain properties.   
Therefore, "the set of all continuous functions from S to S" is a set  
of subsets of SxS.
Received on Tuesday, 12 August 2008 23:23:57 UTC

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