\begin{definition}[Definition:Infimum of Sequence]
A special case of an infimum of a mapping is an '''infimum 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 $\set {x_n: n \in \N}$ admit an infimum.
Then the '''infimum''' of $\sequence {x_n}$) is defined as:
:$\map \inf {\sequence {x_n} } = \map \inf {\set {x_n: n \in \N} }$
\end{definition}