Definition:Bounded Mapping/Real-Valued/Definition 2

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

$f$ is bounded on $S$ :
 * $\exists K \in \R_{\ge 0}: \forall x \in S: \size {\map f x} \le K$

where $\size {\map f x}$ denotes the absolute value of $\map f x$.

Also see

 * Equivalence of Definitions of Bounded Real-Valued Function


 * Definition:Bound of Real-Valued Function