Original sentence: A partially ordered set is a set together with a partial order ≤, i.Every power set P(S) together with inclusion ⊆ is an example of a partially ordered set
Edited sentence: A partially ordered set (poset) is a set together with a partial order ≤, i.Every power set P(S) together with inclusion ⊆ is a partially ordered set.Using the pointwise order on functions between posets, one may alternatively write the extensiveness property as idP ≤ cl