\begin{definition}[Definition:Distance to Nearest Integer Function/Definition 2]
The '''nearest integer function''' $\norm \cdot: \R \to \closedint 0 {\dfrac 1 2}$ is defined as:
:$\norm \alpha:= \min \set {\set \alpha, 1 - \set \alpha}$
where $\set \alpha$ is the fractional part of $\alpha$.
\end{definition}