Suppose 
is a partial ordering on a nonempty set 
. Then the elements 
are said to be comparable provided 
or 
.
Because two elements in a partially ordered set need not be comparable, it is possible for a partially ordered set to have more than one maximal element. For example, suppose
we have a nonempty partially ordered set 
in which every element is incomparable to every other element,
i.e., 
is totally unordered. It follows that every element of 
is maximal.
