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
- 1953: Walter Rudin: Principles of Mathematical Analysis ... (next): $4.13$
- 1975: Bert Mendelson: Introduction to Topology (3rd ed.) ... (previous) ... (next): Chapter $2$: Metric Spaces: $\S 2$: Metric Spaces: Exercise $5$
- 1977: K.G. Binmore: Mathematical Analysis: A Straightforward Approach ... (previous) ... (next): $\S 7.13$