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 $\struct {T, \preceq}$ be an ordered set.

Let $\sequence {x_n}$ be a sequence in $T$.

Let $\sequence {x_n}$ be bounded below in $T$ by $L \in T$.

Then $L$ is a lower bound of $\sequence {x_n}$.

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

Also see

 * Definition:Bounded Below Sequence


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


 * Definition:Bounded Sequence