stylistic:style_transfer
Formal definitions and generalizations

A (non-strict) partial order is a binary relation ≤ over a set P which is reflexive, antisymmetric, and transitive. That is, for all a, b, and c in P, it must satisfy the three following clauses:

A set with a partial order is called a partially ordered set. Those are the very basic axioms that every kind of order has to satisfy.

A strict partial order is a relation < that satisfies:

Some types of partial orders are specified by adding further axioms, such as: