# Definition:Bounded Below Sequence/Real

## Definition

Let $\sequence {x_n}$ be a real sequence.

Then $\sequence {x_n}$ is bounded below if and only if:

$\exists m \in \R: \forall i \in \N: m \le x_i$

### Unbounded Below

$\sequence {x_n}$ is unbounded below if and only if there exists no $m$ in $\R$ such that:

$\forall i \in \N: m \le x_i$