Partially ordered set

In mathematics, especially order theory, a partially ordered set (or poset for short) is a set equipped with a partial order relation. This relation formalizes the intuitive concept of an ordering, sequencing, or arrangement of that set's elements. Such an ordering does not necessarily need to be total, that is, it need not guarantee the mutual comparability of all objects in the set.

Examples

• The set of natural numbers equipped with the lesser than or equal to relation.
• The set of natural numbers equipped with the divides relation.
• The set of subsets of a given set (power set) ordered by inclusion.