Definition:Bounded Below Sequence/Unbounded

Let $\struct {T, \preceq}$ be an ordered set.
Let $\sequence {x_n}$ be a sequence in $T$.
$\sequence {x_n}$ is unbounded below if and only if there exists no $m$ in $T$ such that:
$\forall i \in \N: m \preceq x_i$