Definition:Minimal/Mapping

From ProofWiki
Jump to navigation Jump to search

Definition

Let $f: S \to \R$ be a real-valued function.

Let $f$ be bounded below by a 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


Sources