Definition:Distance to Nearest Integer Function

Definition
The nearest integer function $\| \cdot \| : \R \to [0,1/2]$ defined by one of the following equivalent properties:


 * $\|\alpha \| = \min\{ |n - \alpha| : n \in \Z\}$
 * $\|\alpha \| = \min\{ \{\alpha\},1-\{\alpha\}\}$ where $\{\alpha\}$ is the fractional part of $\alpha$.

The notation $\| \cdot \|_{\R/\Z}$ is also in use.