# Definition:Bounded Below Sequence/Unbounded

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*This page is about Unbounded Below Sequence. For other uses, see Unbounded Below.*

## Definition

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:

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