- published: 25 Dec 2009
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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.
Donald John Trump, Sr. (born June 14, 1946) is an American business magnate, television personality and author. He is the chairman and president of The Trump Organization and the founder of Trump Entertainment Resorts. Trump's extravagant lifestyle, outspoken manner and role on the NBC reality show The Apprentice have made him a well-known celebrity who was No. 17 on the 2011 Forbes Celebrity 100 list. He is well-known as a real-estate developer who amassed vast hotel, casino, and other real-estate properties, in the New York City area and around the world.
Trump is the son of Fred Trump, a wealthy New York City real-estate developer. He worked for his father's firm, Elizabeth Trump & Son, while attending the Wharton School of the University of Pennsylvania, and in 1968 officially joined the company. He was given control of the company in 1971 and renamed it The Trump Organization.
In 2010, Trump expressed an interest in becoming a candidate for President of the United States in the 2012 election. In May 2011, he announced he would not be a candidate, but a few weeks later he said he had not completely ruled out the possibility. In December 2011, Trump was suggested as a possible Vice Presidential selection by Michele Bachmann. Bachmann has since suspended her presidential campaign.