\begin{definition}[Definition:Bounded Sequence]
A special case of a bounded mapping is a '''bounded sequence''', where the domain of the mapping is $\N$.
Let $\struct {T, \preceq}$ be an ordered set.
Let $\sequence {x_n}$ be a sequence in $T$.
Then $\sequence {x_n}$ is '''bounded''' {{iff}} $\exists m, M \in T$ such that $\forall i \in \N$:
:$(1): \quad m \preceq x_i$
:$(2): \quad x_i \preceq M$
That is, {{iff}} it is bounded above and bounded below.
\end{definition}