Contrast With Semilattices
Directed sets are a more general concept than (join) semilattices: every join semilattice is a directed set, as the join or least upper bound of two elements is the desired c. The converse does not hold however, witness the directed set {1000,0001,1101,1011,1111} ordered by binary value (e.g. 1000 ≤ 1011 holds, but 1000 ≤ 0001 does not), where {1000,0001} has three upper bounds but no least upper bound.
Read more about this topic: Directed Set
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