Definition:Bound of Real-Valued Function

This page is about Bound in the context of Real-Valued Function. For other uses, see Bound.

Definition

Let $S$ be a set.

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

Let $f$ be bounded.

Then $B$ is a bound for $f$ if and only if:

$\forall x \in S: B \ge \size {\map f x}$

Sources

• 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)