Unbounded Real-Valued Function/Examples/x sin x

Example of Unbounded Real-Valued Function

The function $f$ defined on the positive real numbers $\openint 0 \to$:

$\forall x \in \openint 0 \to: \map f x := x \sin x$

is both unbounded below and unbounded above.

Hence $f$ is unbounded.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): unbounded function
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): unbounded function