- published: 04 May 2015
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In mathematics, the maximum and minimum (plural: maxima and minima) of a function, known collectively as extrema (singular: extremum), are the largest and smallest value that the function takes at a point either within a given neighborhood (local or relative extremum) or on the function domain in its entirety (global or absolute extremum).
More generally, the maximum and minimum of a set (as defined in set theory) are the greatest and least element in the set. Unbounded infinite sets such as the set of real numbers have no minimum and maximum.
To locate extreme values is the basic objective of optimization.
A real-valued function f defined on a real line is said to have a local (or relative) maximum point at the point x∗, if there exists some ε > 0 such that f(x∗) ≥ f(x) when |x − x∗| < ε. The value of the function at this point is called maximum of the function. Similarly, a function has a local minimum point at x∗, if f(x∗) ≤ f(x) when |x − x∗| < ε. The value of the function at this point is called minimum of the function.
William "Bill" Maher, Jr. ( /ˈmɑːr/; born January 20, 1956) is an American stand-up comedian, television host, political commentator, author, and actor. Before his current role as the host of HBO's Real Time with Bill Maher, Maher hosted a similar late-night talk show called Politically Incorrect originally on Comedy Central and later on ABC.
Maher is known for his political satire and sociopolitical commentary, which targets a wide swath of topics including religion, politics, bureaucracies of many kinds, political correctness, the mass media, greed among people and persons in positions of high political and social power, and the lack of intellectual curiosity in the electorate. He supports the legalization of marijuana and same-sex marriage, and serves on the board of PETA. He is also a critic of religion and is an advisory board member of Project Reason, a foundation to promote scientific knowledge and secular values within society. In 2005, Maher ranked at number 38 on Comedy Central's 100 greatest stand-up comedians of all time. Bill Maher received a Hollywood Walk of Fame star on September 14, 2010.