\begin{definition}[Definition:Divergent Function]
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:
:$\forall H > 0: \exists \delta > 0: \map f x > H$ provided $c < x < c + \delta$
Then (using the language of limits), $\map f x \to +\infty$ as $x \to c^+$.
Let $f: \R \to \R$ be such that:
:$\map f x = \begin {cases}
0 & : x \in \Q \\
1 & : x \notin \Q
\end {cases}$
Then $x$ converges to neither $0$ nor $1$ and hence is '''divergent''' (although, it needs to be noted, not to infinity).
\end{definition}