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In calculus, the extreme value theorem states that if a real-valued function is continuous on the closed and bounded interval , then must attain a maximum and a minimum, each at least once. That is, there exist numbers and in such that: The extreme value theorem is more specific than the related boundedness theorem, which states merely that a ...
Extreme point. A convex set in light blue, and its extreme points in red. In mathematics, an extreme point of a convex set in a real or complex vector space is a point in that does not lie in any open line segment joining two points of In linear programming problems, an extreme point is also called vertex or corner point of [1]
In mathematical analysis, the maximum and minimum[ a ] of a function are, respectively, the largest and smallest value taken by the function. Known generically as extremum, [ b ] they may be defined either within a given range (the local or relative extrema) or on the entire domain (the global or absolute extrema) of a function. [ 1 ][ 2 ][ 3 ...
Extreme value theory is used to model the risk of extreme, rare events, such as the 1755 Lisbon earthquake. Extreme value theory or extreme value analysis ( EVA) is a branch of statistics dealing with the extreme deviations from the median of probability distributions. It seeks to assess, from a given ordered sample of a given random variable ...
The golden ratio is also an algebraic number and even an algebraic integer. It has minimal polynomial. This quadratic polynomial has two roots, and. The golden ratio is also closely related to the polynomial. which has roots and As the root of a quadratic polynomial, the golden ratio is a constructible number.
Limit inferior and limit superior. In mathematics, the limit inferior and limit superior of a sequence can be thought of as limiting (that is, eventual and extreme) bounds on the sequence. They can be thought of in a similar fashion for a function (see limit of a function ). For a set, they are the infimum and supremum of the set's limit points ...
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