Definition:Maximal/Mapping

Definition

Let $f$ be a mapping defined on a subset of the real numbers $S \subseteq \R$.

Let $f$ be bounded above by a supremum $B$.

It may or may not be the case that $\exists x \in S: f \left({x}\right) = B$.

If such a value exists, it is called the maximal value or maximum of $f$ on $S$, and that this maximum is attained at $x$.

Also see

• Minimal

Sources

• K.G. Binmore: Mathematical Analysis: A Straightforward Approach (1977)... (previous)... (next): $\S 7.13$