\begin{definition}[Definition:Nearest Integer Function]
The '''nearest integer function''' is defined as:
:$\forall x \in \R: \nint x = \begin {cases}
\floor {x + \dfrac 1 2} & : x \notin 2 \Z + \dfrac 1 2 \\
x - \dfrac 1 2 & : x \in 2 \Z + \dfrac 1 2
\end{cases}$
where $\floor x$ is the floor function.
{{explain|Definition of $2 \Z$ -- this may help to clarify}}
\end{definition}