In mathematics, the convex hull or convex envelope for a set X of points in the Euclidean plane or Euclidean space is the minimal convex set containing X. For instance, when X is a bounded subset of the plane, the convex hull may be visualized as the shape formed by a rubber band stretched around X. Formally, the convex hull may be defined as the intersection of all convex sets containing X, the intersection of all halfspaces containing X, or the set of all convex combinations of points in X.
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Upper and lower bounds
In mathematics, especially in order theory, an upper bound of a subset S of some partially ordered set (P, ¿) is an element of P which is greater than or equal to every element of S. The term lower bound is defined dually as an element of P which is less than or equal to every element of S. A set with an upper bound is said to be bounded from above by that bound, a set with a lower bound is said to be bounded from below by that bound.
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