A partially ordered set is just a set of objects together with a definition of the "≤" inequality relation, satisfying the axioms of reflexivity ("x" ≤ "x"), antisymmetry (if "x" ≤ "y" and "y" ≤ "x" then "x" = "y") and transitivity (if "x" ≤ "y" and "y" ≤ "z", then "x" ≤ "z"). A total order is a partial order in which, for every two objects "x" and "y" in the set, either "x" ≤ "y" or "y" ≤ "x". Total orders are familiar in computer science as the comparison operators needed to perform comparison sorting algorithms. For finite sets, total orders may be identified with linear sequences of objects, where the "≤" relation is true whenever the first object precedes the second object in the order; a comparison sorting algorithm may be used to convert a total order into a sequence in this way. A linear extension of a partial order is a total order that is compatible with it, in the sense that, if "x" ≤ "y" in the partial order, then "x" ≤ "y" in the total order as well.