A strict weak order on a set is an irreflexive and transitive relation in for which incomparability is transitive. A strict weak order is represented by the Less concept.
Each strict weak order corresponds to a total preorder by , for all , and vice versa. Therefore it is enough to use just one of these concepts. While mathematicians prefer total preorders, the C++ Standard Library is specified using strict weak orders. Using the above correspondence the view can be switched whenever necessary.