>-----Original Message----- >From: Mark A. Biggar [mailto:[EMAIL PROTECTED] >Sent: Sunday, April 13, 2008 11:22 PM >To: Miller, Hugh >Cc: Moritz Lenz; p6l >Subject: Re: cross operator and empty list > >Miller, Hugh wrote: >>> From: Moritz Lenz [mailto:[EMAIL PROTECTED] >>> [EMAIL PROTECTED] wrote: >>>> Technically the Cartesian cross operator doesn't have an >>> identity value. >>> It has. >>> The set which contains only the emty set, or in perl terms ([]); Or >>> am I missing something? >> Should be a (any) 1 point set for the identity. >> How about considering models from category theory, rather than set >> theory ? Seems much more fruitful for computer issues than >set theory. > >No an identity would be a set E such that for any set A: A x E >= A, but no such set exists. A singleton set get close, but >the result is only isomorphic (there is a natural bijection) >not equal. Even in category theory you only get isomorphism. > > >-- >[EMAIL PROTECTED] >[EMAIL PROTECTED] >
Just so! Been looking at category theory so much lately that equality has become just a special case of isomorphism without my noticing it. - Hugh Miller e-mail: [EMAIL PROTECTED]
