\begin{definition}[Definition:Minimum Value of Real Function/Absolute]
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 this '''minimum''' is '''attained at $x$'''.
\end{definition}