Definition:Extremum

Definition

An extremum is an instance of either a greatest or smallest element of an ordered set.

Extremum of Mapping

Let $S$ be a set.

Let $\struct {T, \preccurlyeq}$ be a totally ordered set.

Let $f: S \to T$ be a mapping.

Let $x \in S$ be such that $\map f x$ is an extremum of $\struct {T, \preccurlyeq}$.

Then $x$ is known as an extremum of $f$.

Also see

• Results about extrema can be found here.

Linguistic Note

The plural form of extremum is extrema.

Sources

• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): extremum (plural extrema)