# Definition:Bounded Below Sequence/Unbounded

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*This page is about sequences which are unbounded below. For other uses, see Definition:Unbounded Below.*

## 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:

- $\forall i \in \N: m \preceq x_i$