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).