Definition:Minimal/Mapping

Definition

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

Let $f$ be bounded below by an infimum $B$.

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 minimal value or minimum of $f$ on $S$, and that this minimum is attained at $x$.

Also see

• Maximal

Sources

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