# 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 $\map {\mathrm {nint} } x$.

## Technical Note

The $\LaTeX$ code for $\nint {x}$ is \nint {x} .

When the argument is a single character, it is usual to omit the braces:

\nint x