Editing Directed set (section)

==Contrast with semilattices==
[[File:Directed_set,_but_no_join_semi-lattice.png|thumb|x100px|Example of a directed set which is not a join-semilattice]]

Directed set is a more general concept than (join) semilattice: every [[Semilattice|join semilattice]] is a directed set, as the join or least upper bound of two elements is the desired <math>c.</math>  The converse does not hold however, witness the directed set {1000,0001,1101,1011,1111} [[Coordinatewise order|ordered bitwise]] (e.g. <math>1000 \leq 1011</math> holds, but <math>0001 \leq 1000</math> does not, since in the last bit 1 > 0), where {1000,0001} has three upper bounds but no {{em|least}} upper bound, cf. picture. (Also note that without 1111, the set is not directed.)