³1username³2JoshuaGrosse³2name³2text_default³2version³21³2ts³2980402061³2ip³2129.97.182.64³2data³2newauthor³31³3minor³31³3text³3The standard way of defining a relation R on a set X is as some subset of (X x X).  We write aRb if and only if (a,b) is in R.  Some particularly important kind of relations are MathematicalFunction''s'', EquivalenceRelation''s'', and partial orders (see PartialOrderedSet).

A relation can also be thought of as a function R: (X x X) -> {0,1} where R(x,y)=1 if xRy and R(x,y)=0 if not.  This defines a BooleanAlgebra for the relations on X in a natural way.
³3summary³3³2tscreate³2980402061³2keepts³2980403443³2id³21076³2host³2cnts2p64.uwaterloo.ca³2revision³21³1username³2JoshuaGrosse³2name³2text_default³2version³21³2ts³2980403443³2ip³2129.97.182.64³2data³2text³3The standard way of defining a relation R on a set X is as some subset of (X x X).  We write aRb if and only if (a,b) is in R.  Some particularly important kind of relations are MathematicalFunction''s'', EquivalenceRelation''s'', and partial orders (see PartialOrderedSet).

Relations form a BooleanAlgebra with implications => as the partial order.
³3minor³31³3newauthor³30³3summary³3*³2tscreate³2980402061³2keepts³2980408043³2id³21076³2host³2cnts2p64.uwaterloo.ca³2revision³22³1username³2JoshuaGrosse³2name³2text_default³2version³21³2ts³2980408043³2ip³2129.97.182.33³2data³2newauthor³30³3minor³31³3text³3The standard way of defining a relation R on a set X is as some subset of (X x X).  We write aRb if and only if (a,b) is in R.  Some particularly important kind of relations are MathematicalFunction''s'', EquivalenceRelation''s'', and partial orders (see PartialOrderedSet).
³3summary³3*³2tscreate³2980402061³2keepts³2980442461³2id³21076³2host³2cnts2p33.uwaterloo.ca³2revision³23³1username³2JoshuaGrosse³2name³2text_default³2version³21³2ts³2980442461³2ip³2129.97.130.9³2data³2text³3The standard way of defining a relation R on a set X is as some subset of (X x X).  We write aRb if and only if (a,b) is in R.  Some particularly important kind of relations are MathematicalFunction''s'', EquivalenceRelation''s'', and PartialOrder''s''.
³3minor³31³3newauthor³30³3summary³3*³2tscreate³2980402061³2keepts³2980727724³2id³21076³2host³2cnts3p09.uwaterloo.ca³2revision³24³1username³2JoshuaGrosse³2name³2text_default³2version³21³2ts³2980727724³2ip³2129.97.13.64³2data³2newauthor³30³3minor³31³3text³3The standard way of defining a relation R on a set X is as some subset of (X x X).  We write aRb if and only if (a,b) is in R.  Some particularly important kind of relations are MappinG''s'', EquivalenceRelation''s'', and PartialOrder''s''.
³3summary³3*³2tscreate³2980402061³2keepts³2980729674³2id³21076³2host³2cnts6p64.uwaterloo.ca³2revision³25³1username³2JoshuaGrosse³2name³2text_default³2version³21³2ts³2980729674³2ip³2129.97.13.64³2data³2text³3The standard way of defining a relation R between a set X and a set Y is as some subset of (X x Y).  We write aRb if and only if (a,b) is in R.  Some particularly important kind of relations are MappinG''s'', EquivalenceRelation''s'', and PartialOrder''s''.
³3minor³31³3newauthor³30³3summary³3*³2tscreate³2980402061³2keepts³2980729871³2id³21076³2host³2cnts6p64.uwaterloo.ca³2revision³26³1username³2JoshuaGrosse³2name³2text_default³2version³21³2ts³2980729871³2ip³2129.97.13.64³2data³2newauthor³30³3minor³31³3text³3The standard way of defining a relation R between a set X and a set Y is as some subset of (X x Y).  We write aRb if and only if (a,b) is in R.  This can also be looked at as a mapping from (X x Y) to 2={0,1}.

Some particularly important kind of relations are MappinG''s'', EquivalenceRelation''s'', and PartialOrder''s''.
³3summary³3*³2tscreate³2980402061³2keepts³2980730067³2id³21076³2host³2cnts6p64.uwaterloo.ca³2revision³27