# Extreme

This crossword clue is for the definition: Extreme.
it’s A 7 letters crossword puzzle definition.
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Last seen on: LA Times Crossword 9 Jun 2018, Saturday

### Random information on the term “Extreme”:

In mathematics, an extreme point of a convex set S in a real vector space is a point in S which does not lie in any open line segment joining two points of S. Intuitively, an extreme point is a “vertex” of S.

The Krein–Milman theorem is stated for locally convex topological vector spaces. The next theorems are stated for Banach spaces with the Radon–Nikodym property:

Let E be a Banach space with the Radon-Nikodym property, let C be a separable, closed, bounded, convex subset of E, and let a be a point in C. Then there is a probability measure p on the universally measurable sets in C such that a is the barycenter of p, and the set of extreme points of C has p-measure 1.

Edgar’s theorem implies Lindenstrauss’s theorem.

More generally, a point in a convex set S is k-extreme if it lies in the interior of a k-dimensional convex set within S, but not a k+1-dimensional convex set within S. Thus, an extreme point is also a 0-extreme point. If S is a polytope, then the k-extreme points are exactly the interior points of the k-dimensional faces of S. More generally, for any convex set S, the k-extreme points are partitioned into k-dimensional open faces.

### Random information on the term “END”:

The word “value” is both a verb and a noun, each with multiple meanings. But its root meaning always involves social judgments of qualities such as goodness, worth, truth, justice, beauty. The word names either the rational criterion applied when judging, or results of judging, the presence of such qualities.:1-3:37–44

Humans attribute qualities to objects, beliefs, and behaviors as they identify means that “work” to carry on social life, and ends that are “right” for social life itself. Qualities that “work” are judged by the instrumental criterion, and are said to possess instrumental value. Qualities that are “right” in themselves are judged by the intrinsic criterion, and are said to possess intrinsic value. The value of a smart phone or a scientific theory is instrumental. The value of the Ten Commandments or the US Constitution is intrinsic.

The noun value sometimes names the instrumental or intrinsic criterion being applied. More often, it names things judged to possess instrumental or intrinsic value. Modern scholars have refined these ancient common-sense meanings of value. Sociologist Max Weber applied the labels instrumental and intrinsic value to two patterns of social action. Here are his original definitions, followed by current labels for the two criteria from the Oxford Handbook of Value Theory.