Definition:Distance to Nearest Integer Function/Definition 2

Definition
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 $\alpha$.