Definition:Strictly Ordered Set

Definition
A strictly ordered set is a relational structure $\left({S, \prec}\right)$ such that the relation $\prec$ is an strict ordering.

Such a structure may be:


 * A linearly ordered set (loset)
 * A strictly well-ordered set

depending on whether the ordering $\preceq$ is:


 * A strict total ordering
 * A strict well-ordering.