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.

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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

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

Sources

• Weisstein, Eric W. "Nearest Integer Function." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/NearestIntegerFunction.html