Divergent Function/Examples/Tending to Infinity

Example of Divergent Function

Let $f: \R \to \R$ be such that:

$\forall H > 0: \exists \delta > 0: \map f x > H$ provided $c < x < c + \delta$

Then (using the language of limits), $\map f x \to +\infty$ as $x \to c^+$.

That is, $f$ is divergent at $c$.