Definition:Minimum Value of Real Function/Absolute

Definition
Let $f: \R \to \R$ be a real function.

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

It may or may not be the case that $\exists x \in \R: \map f x = B$.

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

Also known as
An absolute minimum is also known as a minimum value, or just a minimum if there is no need to distinguish it from a local minimum.

Also see

 * Definition:Local Minimum


 * Definition:Local Maximum
 * Definition:Absolute Maximum