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 a poset.

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 $H \in T$.

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

Also see

 * Definition:Bounded Below Sequence


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


 * Definition:Bounded Sequence