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.
