# Definition:Minimal/Mapping

< Definition:Minimal(Redirected from Definition:Minimal Value)

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## 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

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