A partially ordered set (or ordered set or poset for short) is called a complete lattice if every subset of has a least upper bound (supremum, ) and a greatest lower bound (infimum, ) in .
Taking shows that every complete lattice has a greatest element (maximum, ) and a least element (minimum, ).
Of course, every complete lattice is a lattice. Moreover, every lattice with a finite set is a complete lattice.