Definition:Divergent Function

Definition
A function which is not convergent is divergent.

There are multiple ways that a function can be divergent. Here are some samples:


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


 * $\forall H > 0: \exists \delta > 0: f \left({x}\right) > H$ provided $c < x < c + \delta$

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


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


 * $f \left({x}\right) = \begin{cases}

0 & : x \in \Q \\ 1 & : x \notin \Q \end{cases}$

Then $x$ converges to neither $0$ nor $1$ and hence is divergent (although, it needs to be noted, not to infinity).