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Concave set

 

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Concave set



 
 
In mathematics
Mathematics

Mathematics is the study of quantity, structure, space, change, and related topics of pattern and form. Mathematicians seek out patterns whether found in numbers, space, natural science, computers, imaginary abstractions, or elsewhere....
, the notion of concave set is complementary to that of the convex set
Convex set

In Euclidean space, an object is convex if for every pair of points within the object, every point on the straight line segment that joins them is also within the object....
.

The following definitions are in use.










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In mathematics
Mathematics

Mathematics is the study of quantity, structure, space, change, and related topics of pattern and form. Mathematicians seek out patterns whether found in numbers, space, natural science, computers, imaginary abstractions, or elsewhere....
, the notion of concave set is complementary to that of the convex set
Convex set

In Euclidean space, an object is convex if for every pair of points within the object, every point on the straight line segment that joins them is also within the object....
.

The following definitions are in use.

  • A set is called concave if it is not convex.
  • A set is called concave if its complement
    Complement

    In many different fields, the complement of X is something that together with X makes a complete whole, something that supplies what X lacks....
     is convex.


See also

  • Concave function
    Concave function

    In mathematics, a concave function is the additive inverse of a convex function. A concave function is also synonymously called concave downwards, concave down, convex cap or upper convex....