Operations
==========

The definitions in this section extend what can be done with :ref:`sets<set-theory>` by allowing means of combining elements from the sets.

.. prf:definition:: Operation
   :label: def:operation

   For any :prf:ref:`set<def:set>`, :math:`A`, an operation, :math:`*` on :math:`A` is a rule which assigns exactly one element of the set :math:`A` to a pair of elements from :math:`A`.

.. prf:example:: Addition on the integers

   Addition is a rule which takes any two integers and produces a third integer.