Extreme Lives

Extreme Lives
Extreme may refer to: Science and mathematics Mathematics * Extreme point, a point in a convex set which does not lie in any open line segment joining two points in the set * Maxima and minima, extremes on a mathematical function Science * Extremophile, an organism which thrives in or requires "extreme" * Extremes on Earth *List of extrasolar planet extremes Politics * Extremism, political ideologies or actions deemed outside the acceptable range *The Extreme (Italy) The Historical Far Left ( it, Estrema Sinistra Storica), originally known as Far Left ( it, Estrema Sinistra), Radical Extreme ( it, Estrema Radicale), simply The Extreme ( it, L'Estrema), or Party of Democracy ( it, Partito della Democrazia), wa ... or Historical Far Left, a left-wing parliamentary group in Italy 1867–1904 Business * Extreme Networks, a California-based networking hardware company * Extreme Records, an Australia-based record label * Extreme Associates, a California-based adult film studio C ...
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Extreme Point
In mathematics, an extreme point of a convex set S in a real or complex vector space is a point in S which does not lie in any open line segment joining two points of S. In linear programming problems, an extreme point is also called vertex or corner point of S. Definition Throughout, it is assumed that X is a real or complex vector space. For any p, x, y \in X, say that p x and y if x \neq y and there exists a 0 < t < 1 such that

p = t x + (1-t) y.

K

is a subset of

X

and

p \in K,

then

p

is called an of

K

if it does not lie between any two points of

K.

That is, if there does exist

x, y \in K

and

0 < t < 1

such that

x \neq y

and

p = t x + (1-t) y.

The set of all extreme points of

K

is denoted by

\operatorname(K).

Generalizations If

S

is a subset of a vector space then a linear sub ...
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