\begin{definition}[Definition:Oscillating Sequence]
Let $S$ be one of the standard number fields $\Q$, $\R$ or $\C$.
Let $\sequence {x_n}$ be a sequence in $S$.
Let $\sequence {x_n}$ be divergent.
Suppose $\sequence {x_n}$ is ''not'' unbounded.
That is, let:
:$\neg x_n \to \infty$ as $n \to \infty$
Then $\sequence {x_n}$ is said to '''oscillate'''.
\end{definition}