n. (Logic) any of a number of categories of relations that permit at least some members of their domain to be placed in order. A linear ordering (or simple ordering) is reflexive, antisymmetric, transitive and connected (complete), and thus enables every member to be ordered relative to every other; for example, less than or equal to on the integers. A partial ordering is reflexive, antisymmetric and transitive, and thus generates chains of comparable elements; members of distinct chains may be incomparable, as with set inclusion. Either of these orderings is strongor strict if it is asymmetric instead of reflexive and antisymmetric, such as strictly less than, or proper set inclusion. An ordering is a well-ordering if every non-empty subset has a least member under the ordering, i.e. a unique member that has the given relation to all other members of the subset. A pre-ordering or quasi-orderingis reflexive and transitive. The reverse orderingsets a less than (or equal to) b exactly when b is less than (or equal to) a. There is much variation in the usage of these terms. See also lattice, partial order, tree.