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.

Also known as
Some sources refer to $\struct {S, \prec}$ as a strict partial order, calling $\preceq$ a strict partial order relation.

Also see

 * Definition:Ordered Set
 * Definition:Partially Ordered Set
 * Definition:Totally Ordered Set
 * Definition:Well-Ordered Set


 * Definition:Strictly Partially Ordered Set
 * Definition:Strictly Totally Ordered Set
 * Definition:Strictly Well-Ordered Set