Definition:Bounded Mapping/Real-Valued/Unbounded

Definition

Let $S$ be a set.

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

$f$ is unbounded if and only if it is neither bounded above nor bounded below.

Examples

Example: $-1^n n$

The function $f$ defined on the integers $\Z$:

$\forall x \in \Z: f := \paren {-1}^n n$

is unbounded.

Also see

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

Sources

• 1970: Arne Broman: Introduction to Partial Differential Equations ... (previous) ... (next): Chapter $1$: Fourier Series: $1.1$ Basic Concepts: $1.1.2$ Definitions