In computing, NaN, standing for not a number, is a member of a numeric data type that can be interpreted as a value that is undefined or unrepresentable, especially in floating-point arithmetic.

In computer science and computer programming, a data type or simply type is an attribute of data which tells the compiler or interpreter how the programmer intends to use the data.

In computing, floating-point arithmetic is arithmetic using formulaic representation of real numbers as an approximation to support a trade-off between range and precision.

Computing is any goal-oriented activity requiring, benefiting from, or creating a mathematical sequence of steps known as an algorithm — e.g. through computers.

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Systematic use of NaNs was introduced by the IEEE 754 floating-point standard in 1985, along with the representation of other non-finite quantities such as infinities.

IEEE 754-1985 was an industry standard for representing floating-point numbers in computers, officially adopted in 1985 and superseded in 2008 by IEEE 754-2008, and then again in 2019 by minor revision IEEE 754-2019.

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In mathematics, zero divided by zero is undefined as a real number, and is therefore represented by NaN in computing systems.

Mathematics is the study of topics such as quantity, structure, space, and change.


The square root of a negative number is not a real number in mathematics, so is represented by NaN in compliant computing systems.

In mathematics, a square root of a number x is a number y such that y2 = x; in other words, a number y whose square is x.


NaNs may also be used to represent missing values in computations.


Two separate kinds of NaNs are provided, termed quiet NaNs and signaling NaNs.


Quiet NaNs are used to propagate errors resulting from invalid operations or values.


Signaling NaNs can support advanced features such as mixing numerical and symbolic computation or other extensions to basic floating-point arithmetic.

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