Definition:Bounded Below Sequence/Real/Unbounded

Definition
Let $\left \langle {x_n} \right \rangle$ be a real sequence.

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