\begin{definition}[Definition:Infimum of Real Sequence]
Let $\sequence {x_n}$ be a real sequence.
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}