\begin{definition}[Definition:Lower Bound of Sequence]
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 $\sequence {x_n}$'''.
\end{definition}