Definition:Nearest Integer Function

Definition
The nearest integer function is defined as:
 * $\forall x \in \R : \operatorname{nint}(x)=

\begin{cases} \left\lfloor x + \frac12 \right\rfloor & : x \notin 2 \Z + \frac12 \\ x - \frac12 & : x \in 2 \Z + \frac12 \end{cases}$ where $\left\lfloor x \right\rfloor$ is the floor function.

Also denoted as
The nearest integer function can also be denoted $\lfloor\cdot\rceil$ or $[\cdot]$. Because $[\cdot]$ is also sometimes used to denote the floor function, its use may lead to confusion.

Also see

 * Definition:Floor Function
 * Definition:Ceiling Function
 * Definition:Fractional Part
 * Definition:Distance to Nearest Integer Function