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:
“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)
“The comparison between Coleridge and Johnson is obvious in so far as each held sway chiefly by the power of his tongue. The difference between their methods is so marked that it is tempting, but also unnecessary, to judge one to be inferior to the other. Johnson was robust, combative, and concrete; Coleridge was the opposite. The contrast was perhaps in his mind when he said of Johnson: “his bow-wow manner must have had a good deal to do with the effect produced.””
—Virginia Woolf (1882–1941)