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)
“Flowers and fruits are always fit presents; flowers, because they are a proud assertion that a ray of beauty outvalues all of the utilities of the world. These gay natures contrast with the somewhat stern countenance of ordinary nature: they are like music heard out of a work-house.”
—Ralph Waldo Emerson (1803–1882)