\begin{definition}[Definition:Bounded Above Sequence]
Let $\struct {T, \preceq}$ be an ordered set.
Let $\sequence {x_n}$ be a sequence in $T$.
Then $\sequence {x_n}$ is '''bounded above''' {{iff}}:
:$\exists M \in T: \forall i \in \N: x_i \preceq M$
\end{definition}