Minority Report (film) Minority Report (film) Minority Report is a 2002 American neo-noir science fiction film directed by Steven Spielberg and loosely based on the short story "The Minority Report" by Philip K. Dick. It is set primarily in Washington, D.C., and Northern Virginia in the year 2054, where PreCrime, a specialized police department, apprehends criminals based on foreknowledge provided by three psychics called "precogs". The cast includes Tom Cruise as Chief of PreCrime John Anderton, Colin Farrell as Department of Justice agent Danny Witwer, Samantha Morton as the senior precog Agatha, and Max von Sydow as Anderton's superior Lamar Burgess. The film
Directed set Directed set In mathematics, a directed set (or a directed preorder or a filtered set) is a nonempty set "A" together with a reflexive and transitive binary relation ≤ (that is, a preorder), with the additional property that every pair of elements has an upper bound. In other words, for any "a" and "b" in "A" there must exist "c" in "A" with "a" ≤ "c" and "b" ≤ "c". The notion defined above is sometimes called an upward directed set. A downward directed set is defined analogously, meaning when every pair of elements is bounded below. Some authors (and