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
Famous quotes containing the word contrast:
“By contrast with history, evolution is an unconscious process. Another, and perhaps a better way of putting it would be to say that evolution is a natural process, history a human one.... Insofar as we treat man as a part of nature—for instance in a biological survey of evolution—we are precisely not treating him as a historical being. As a historically developing being, he is set over against nature, both as a knower and as a doer.”
—Owen Barfield (b. 1898)