Definition:Distance to Nearest Integer Function/Definition 1

Definition
The nearest integer function $\norm \cdot: \R \to \closedint 0 {\dfrac 1 2}$ is defined as:
 * $\norm \alpha:= \min \set {\size {n - \alpha}: n \in \Z}$

Also see

 * Equivalence of Definitions of Distance to Nearest Integer Function