Definition:Bounded Below Sequence/Unbounded

Definition
Let $\struct {T, \preceq}$ be an ordered set.

Let $\sequence {x_n}$ be a sequence in $T$.

$\sequence {x_n}$ is unbounded below there exists no $m$ in $T$ such that:
 * $\forall i \in \N: m \preceq x_i$