Definition:Nearest Integer Function
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Definition of $2 \Z$ -- this may help to clarify
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Contents
Definition
The nearest integer function is defined as:
- $\forall x \in \R: \operatorname{nint} \left({x}\right) = \begin{cases} \left\lfloor{x + \dfrac 1 2}\right\rfloor & : x \notin 2 \Z + \dfrac 1 2 \\ x - \dfrac 1 2 & : x \in 2 \Z + \dfrac 1 2 \end{cases}$
where $\left\lfloor{x}\right\rfloor$ is the floor function.
Definition of $2 \Z$ -- this may help to clarify
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Also denoted as
The nearest integer function can also be denoted $\left\lfloor{\cdot}\right\rceil$ or $\left[{\cdot}\right]$.
Because $\left[{\cdot}\right]$ has, in earlier times, been 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
Sources
- Weisstein, Eric W. "Nearest Integer Function." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/NearestIntegerFunction.html
