Definition:Bounded Below Sequence

Definition
Let $\left({T, \preceq}\right)$ be an ordered set.

Let $\left \langle {x_n} \right \rangle$ be a sequence in $T$.

Then $\left \langle {x_n} \right \rangle$ is bounded below iff:
 * $\exists m \in T: \forall i \in \N: m \preceq x_i$

Real Sequence
The concept is usually encountered where $\left({T, \preceq}\right)$ is the set of real numbers under the usual ordering: $\left({\R, \le}\right)$:

Also see

 * Definition:Bounded Above Sequence
 * Definition:Bounded Sequence


 * Definition:Bounded Below Mapping, of which a bounded below sequence is the special case where the domain of the mapping is $\N$.


 * Definition:Lower Bound of Sequence