Definition:Lower Bound of Sequence

Definition
A special case of a lower bound of a mapping is a lower bound of a sequence, where the domain of the mapping is $\N$.

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

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

Let $\left \langle {x_n} \right \rangle$ be bounded below in $T$ by $L \in T$.

Then $L$ is a lower bound of $\left \langle {x_n} \right \rangle$.

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 Below Sequence


 * Definition:Bounded Above Sequence
 * Definition:Upper Bound of Sequence


 * Definition:Bounded Sequence