Definition:Nearest Integer Function

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

\floor {x + \dfrac 1 2} & : x \notin 2 \Z + \dfrac 1 2 \\ x - \dfrac 1 2 & : x \in 2 \Z + \dfrac 1 2 \end{cases}$ where $\floor x$ is the floor function.

Also denoted as
The nearest integer function can also be denoted $\sqbrk {\, \cdot \,}$ but because is also frequently seen for the floor function, its use may lead to confusion.

Some sources use the more explicit $\map {\mathrm {nint} } x$.

Also see

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