I learned the definition a set being complete as below.
An ordered set (X, =<) is said to be complete if for every non-empty subset of X which is bounded above (or below), there exists a supremum (or infimum).
But I'm not sure if an "ordered set" means only a totally ordered set or both a totally ordered set a partially ordered set. If it means the latter, I don't understand how a partially ordered set can be complete. Because I understood a partially ordered set can have elements which are not comparable and so there may not exist a supremum or infimum.
Does an "ordered set" mean only a totally ordered set or both a totally ordered set and a partially ordered set? And could you give me an example if it is the latter?