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Mathematics-Online lexicon: | ||
Properties of Relations |
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z | overview |
A reflexive, symmetric and transitive relation is called an
equivalence relation, usually symbolized by instead of
. An equivalence relation divides a set
in
disjoint subsets (equivalence classes), with any two elements of a
particular subset being related (equivalent) to each other, while
two elements of distinct subsets are not related to one another.
A reflexive, asymmetric and transitive relation is called a partial
order, symbolized as instead of
. If
a partial order is complete, it is called a (total) order;
is
then ordered by
.
automatically generated 6/19/2007 |