Definition:Bounded Sequence/Real

Definition
Let $\left \langle {x_n} \right \rangle$ be a real sequence.

Then $\left \langle {x_n} \right \rangle$ is bounded iff $\exists m, M \in \R$ such that $\forall i \in \N$:
 * $m \le x_i$
 * $x_i \le M$

That is, iff it is bounded above and bounded below.