Definition:Bounded Above Sequence

Definition
A special case of a bounded above mapping is a bounded above sequence, where the domain of the mapping is $\N$.

Let $\left({T, \preceq}\right)$ be a poset.

Let $\left \langle {x_n} \right \rangle$ be a sequence in $T$.

Then $\left \langle {x_n} \right \rangle$ is bounded above iff:
 * $\exists M \in T: \forall i \in \N: x_i \preceq M$

If there is no such $M \in T$ then $\left \langle {x_n} \right \rangle$ is unbounded above.

Also see

 * Bounded Below Sequence
 * Bounded Sequence