Definition:Oscillating Sequence

Definition
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 divergent to $\infty$.

That is, let:
 * $\neg x_n \to \infty$ as $n \to \infty$

Then $\sequence {x_n}$ is said to oscillate.

Also see
An example is the sequence $\sequence {x_n}$ where $x_n = \paren {-1}^n$ as demonstrated in Divergent Sequence may be Bounded.