- For a partial-ordered set, I was wondering if the least-upper-bound/greatest-lower-bound property means that any nonempty subset that has an upper/lower bound has a least-upper/greatest-lower bound, or any subset that has an upper/lower bound has a least-upper/greatest-lower bound? Is least-upper-bound property also called Dedekind completeness?
Why is the following statement true:
A partial ordered set has the least upper bound property if and only if it has the greatest lower bound property.
Thanks and regards!