 Note that this is not just a property of the set "S" but also one of the set "S" as subset of "P".A bounded poset "P" (that is, by itself, not as subset) is one that has a least element and a greatest element.Note that this concept of boundedness has nothing to do with finite size, and that a subset "S" of a bounded poset "P" with as order the restriction of the order on "P" is not necessarily a bounded poset.