Jeremy Irons Dragons" (2000) and Rupert Gould in "Longitude" (2000). He played the Über-Morlock in the film "The Time Machine" (2002). In 2004, Irons played Severus Snape in Comic Relief's "Harry Potter" parody, "Harry Potter and the Secret Chamberpot of Azerbaijan". In 2005, he appeared in the films "Casanova" opposite Heath Ledger, and Ridley Scott's "Kingdom of Heaven". He has co-starred with John Malkovich in two films, "The Man in the Iron Mask" (1998) and "Eragon" (2006), though they did not have any scenes together in the latter. In 2008, Irons co-starred with Ed Harris and Viggo Mortensen in "Appaloosa", directed by
Directed set bound of two elements is the desired "c". The converse does not hold however, witness the directed set {1000,0001,1101,1011,1111} ordered bitwise (e.g. 1000 ≤ 1011 holds, but 0001 ≤ 1000 does not, since in the last bit 1 > 0), where {1000,0001} has three upper bounds but no "least" upper bound, cf. picture. (Also note that without 1111, the set is not directed.) The order relation in a directed set is not required to be antisymmetric, and therefore directed sets are not always partial orders. However, the term "directed set" is also used frequently in the context of posets. In