Technologies in Minority Report "Minority Report" were handled by Jeff Boortz of Concrete Pictures, who said "the whole idea, from a script point of view, was that the advertisements would recognize you -- not only recognize you, but recognize your state of mind. It's the kind of stuff that's going on now with digital set-top boxes and the Internet." Nokia designed the phones used by the characters, and Lexus paid the producers $5 million for the rights to design the futuristic "Mag-Lev" cars. All told money raised through product placement accounted for $25 million of the film's $102 million production budget. Spielberg described his
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