Definition:Oscillating Sequence

Definition
Let $$\left \langle {x_n} \right \rangle$$ be a sequence in $$\R$$ or $$\C$$.

Let $$\left \langle {x_n} \right \rangle$$ be divergent.

Suppose $$\left \langle {x_n} \right \rangle$$ is not divergent to $\infty$.

That is, let:
 * $$x_n \not\to \infty$$ as $$n \to \infty$$.

Then $$\left \langle {x_n} \right \rangle$$ is said to oscillate.

An example is the sequence $$\left \langle {x_n} \right \rangle$$ where $$x_n = \left({-1}\right)^n$$ as demonstrated in Divergent Sequences may be Bounded.