\begin{definition}[Definition:Bounded Sequence/Real]
Let $\sequence {x_n}$ be a real sequence.
Then $\sequence {x_n}$ 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.
\end{definition}