Definition:Bounded Mapping/Real-Valued/Definition 1
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Definition
Let $f: S \to \R$ be a real-valued function.
$f$ is bounded on $S$ if and only if:
- $f$ is bounded above on $S$
and also:
- $f$ is bounded below on $S$.
Also see
- Results about bounded real-valued functions can be found here.
Sources
- 1947: James M. Hyslop: Infinite Series (3rd ed.) ... (previous) ... (next): Chapter $\text I$: Functions and Limits: $\S 3$: Bounds of a Function
- 1977: K.G. Binmore: Mathematical Analysis: A Straightforward Approach ... (previous) ... (next): $\S 7.13$
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): bound: 1. (of a function)
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): bound: 1. (of a function)