Minority Report (film) its ending. The film has a more traditional "happy ending" which contradicts the tone of the rest of the picture. This has led to speculation that this ending is the product of John's imagination, caused by hallucinations from his forced coma after he is incarcerated. As one observer mused, "The conclusion of "Minority Report" strikes me as a joke Spielberg played on his detractors—an act of perfectly measured deviltry." One critic theorized, "...[r]ather than end this "Brazil"-ian sci-fi dystopia with the equivalent of that film's shot of its lobotomized hero, which puts the lie to the immediately previous scene of
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