any of a number of categories of relations that permit at least some members of their domain to be placed in order. A linear or simple ordering is reflexive, antisymmetric, transitive, and connected, as less than or equal to on the integers. A partial ordering is reflexive, antisymmetric, and transitive, as set inclusion. Either of these orderings is called strict if it is asymmetric instead of reflexive and antisymmetric. It is a well-ordering if every nonempty subset has a least member under the relation