Definition:Bounded Below Sequence/Unbounded

Definition
Let $\left({T, \preceq}\right)$ be an ordered set.

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

$\left \langle {x_n} \right \rangle$ is unbounded below iff there exists no $m$ in $T$ such that:
 * $\forall i \in \N: m \preceq x_i$