Definition:Partially Ordered Set

A poset (convenient abbreviation for partially ordered set) is a relational structure $$\left({S; \preceq}\right)$$ such that "$$\preceq$$" is an Ordering (which, by definition, is allowed to be "partial").

The poset $$\left({S; \preceq}\right)$$ is said to be partially ordered by $$\preceq$$.