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 this article) assume that a directed set is directed upward, unless otherwise stated. Beware that other authors call a set directed if and only if it is directed both upward and downward. Directed sets are a generalization of nonempty totally ordered sets. That is, all totally ordered sets are directed sets (contrast "partially" ordered sets, which need not be directed). Join semilattices (which are partially ordered sets) are directed sets as well, but not conversely. Likewise, lattices are directed sets both upward and downward. In topology, directed sets are used to define nets, which generalize sequences and unite the various