Re: How is this collection called?
From: Mikito Harakiri <mikharakiri_at_iahu.com>
Date: Tue, 30 Mar 2004 08:27:46 -0800
Message-ID: <Knhac.12$mR.34_at_news.oracle.com>
Date: Tue, 30 Mar 2004 08:27:46 -0800
Message-ID: <Knhac.12$mR.34_at_news.oracle.com>
"Paul" <pbrazier_at_cosmos-uk.co.uk> wrote in message
news:51d64140.0403300727.2ef94b6_at_posting.google.com...
> Define a*b as "a U {b}" (where U is set union)
> Then a*(b*c) = aU{bU{c}} != (a*b)*c = aU{b}U{c}.
I wonder how your example works. It reminds me Kuratowski's definition of
ordered pair
(a,b) = {{a}, {a,b}}
Formally,
((a,b),c)={ {{a}, {a,b}}, {{{a}, {a,b}} ,{c}} }
(a,(b,c))={ {{b}, {b,c}}, {{{b}, {b,c}} ,{a}} }
are different sets, but we still consider them isomorphic. There was a
recent thread on sci.math "Question about associativity of cartesian
product".