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MathematicalRelation

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.