Strict weak ordering is a binary relation on a set. Such relations define a strict ordering, but they contain several elements of the same type. An example might be the relation "costs less than", or "is cheaper than". For any two elements that are "of different types", the relation holds. On the other hand, there are some elements that cannot be ordered that way, because they are of the same type. An example for such a relation may be the relation, "costs less than": milk may "cost less than" bread, and bread may cost less than cake. Two items of different types may cost less than another, but they can otherwise have the same price.