Definition:Bounded Below Sequence

Definition
A special case of a bounded below mapping is a bounded below 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 below iff:
 * $\exists m \in T: \forall i \in \N: m \preceq x_i$

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

Also see

 * Definition:Bounded Above Sequence
 * Definition:Bounded Sequence