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 words contrast with and/or contrast:
“In contrast with envy, which usually occurs between two people and is focused upon another person’s qualities or possessions, jealousy occurs when a third person becomes a threat to a dyad. Jealousy involves the loss or the impending loss of a relationship that one wants to hold onto, a relationship that is vital to personal fulfillment and claimed as one’s own.”
—Carol S. Becker (b. 1942)
“Armies, for the most part, are made up of men drawn from simple and peaceful lives. In time of war they suddenly find themselves living under conditions of violence, requiring new rules of conduct that are in direct contrast to the conditions they lived under as civilians. They learn to accept this to perform their duties as fighting men.”
—Gil Doud, U.S. screenwriter, and Jesse Hibbs. Walter Bedell Smith (Himself)