Minority Report (film) alone and with Tom Cruise; together they conferred publicly with Ron Howard and Russell Crowe via a similar webcam on the set of "A Beautiful Mind" in New York. The location of the small, uncharted island in the last shot of the film is Butter Island off North Haven, Maine in the Penobscot Bay. Although it takes place in an imagined future world of advanced technology, "Minority Report" attempts to embody a more "realistic" depiction of the future. Spielberg decided that to be more credible, the setting had to keep both elements of the present and ones which specialists expected
Directed set While the definition of a directed set is for an "upward-directed" set (every pair of elements has an upper bound), it is also possible to define a downward-directed set in which every pair of elements has a common lower bound. A subset of a poset is downward-directed if and only if its upper closure is a filter. Directed subsets are used in domain theory, which studies directed complete partial orders. These are posets in which every upward-directed set is required to have a least upper bound. In this context, directed subsets again provide a generalization of convergent sequences. Directed set