Definition:Bounded Mapping/Real-Valued/Definition 2

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Definition

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


$f$ is bounded on $S$ if and only if:

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

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


Also see

  • Results about bounded real-valued functions can be found here.


Sources