Definition:Bounded Mapping/Real-Valued/Definition 2

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

$f$ is bounded on $S$ :
 * $\exists K \in \R_{\ge 0}: \forall x \in S: \left\vert{f \left({x}\right)}\right\vert \le K$

where $\left\vert{f \left({x}\right)}\right\vert$ denotes the absolute value of $f \left({x}\right)$.

Also see

 * Equivalence of Definitions of Bounded Real-Valued Function


 * Definition:Bound of Real-Valued Function