Wikipedia 10K Redux by Reagle from Starling archive. Bugs abound!!!

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The 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.