There are several categorizations of binary relations based on which
axioms they hold. These are called orders.
* preorder
* weak order
* strict weak order
* strict order
* strict partial order
* equivalence
From the orderings a framework is built up.
* strict order
* weak order
Examples:
* subset on all sets is a preorder
* => on R is a strict order
* "=>" on R^2 is a antisymmetric preorder
* || || (magnitude) on R^2 is a weak order