You are thinking of a total order (in fact total orderings or often defined with the '>=' relation). A partial order is like a total order except there may be s

You are thinking of a total order (in fact total orderings or often defined with the '>=' relation). A partial order is like a total order except there may be some elements that are not comparable, so given elements {A, B, C} we can have C < A and C < B but whether A < B or B < A can remain undefined. A lattice is a kind of partially ordered set.