ickeextremal

Ickeextremal is a term encountered in some mathematical discussions to denote an element that is not extremal with respect to a given structure. Because there is no universally standardized definition, the precise meaning of ickeextremal can vary by context, but it generally serves as the antonym of extremal within the same framework.

In order-theoretic contexts, an element is considered extremal if it is minimal or maximal within a poset (depending on the chosen convention). An element that is neither minimal nor maximal is often described as ickeextremal. For example, in a finite chain 1 < 2 < ... < n, the end points 1 and n are extremal, while the interior elements 2 through n−1 are ickeextremal.

In convex geometry, an extremal (or extreme) point of a convex set is one that cannot be written as a convex combination of other points in the set. Points that can be expressed as such convex combinations are non-extreme or ickeextremal relative to that set. Thus, interior points of a convex polygon or polytope are typically ickeextremal, whereas the polygon’s vertices are extremal.

Because ickeextremal is not a universally standardized term, researchers sometimes prefer phrases like non-extremal or non-extreme to convey the same idea. The usage of ickeextremal often appears in informal discussions or in contexts where a playful or language-inspired prefix is employed.

See also extremal, extreme point, convex hull, non-extremal, minimal element, maximal element.