.. _relations:

Relations
=========

Just as sets provide a convenient language for properties of the objects in a type,
*relations* provide a convenient language for the properties of the pairs of objects
in a type.  This might sound dry and abstract, but such properties turn up all over
mathematics: the property of one real
number being less than another; the property of one integer being congruent to
another modulo 5; the property of one set being a subset of another; the property
of one function being inverse to another.

In this chapter we introduce some of the important properties which relations
themselves can have: they can be *reflexive*, *symmetric*, *antisymmetric* or
*transitive*, or any combination of these.

.. include:: ch10_Relations/01_Introduction.inc
.. include:: ch10_Relations/02_Equivalence_Relations.inc