Definition:Ordered Set

Definition
An ordered set is a relational structure $$\left({S; \preceq}\right)$$ such that the relation $$\preceq$$ is an ordering.

Such a structure may be:


 * A partially ordered set (poset);
 * A totally ordered set (toset);
 * A well-ordered set (woset)

depending on whether the ordering $$\preceq$$ is:


 * A partial ordering;
 * A total ordering;
 * A well-ordering.