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### 19.7 Mathematical Constants

— Built-in Variable: I
— Built-in Variable: J
— Built-in Variable: i
— Built-in Variable: j

A pure imaginary number, defined as sqrt (-1). These built-in variables behave like functions so you can use the names for other purposes. If you use them as variables and assign values to them and then clear them, they once again assume their special predefined values See Status of Variables.

— Built-in Variable: Inf
— Built-in Variable: inf

Infinity. This is the result of an operation like 1/0, or an operation that results in a floating point overflow.

— Built-in Variable: NaN
— Built-in Variable: nan

Not a number. This is the result of an operation like 0/0, or `Inf - Inf', or any operation with a NaN.

Note that NaN always compares not equal to NaN. This behavior is specified by the IEEE standard for floating point arithmetic. To find NaN values, you must use the isnan function.

— Built-in Variable: pi

The ratio of the circumference of a circle to its diameter. Internally, pi is computed as `4.0 * atan (1.0)'.

— Built-in Variable: e

The base of natural logarithms. The constant e satisfies the equation log (e) = 1.

— Built-in Variable: eps

The machine precision. More precisely, eps is the largest relative spacing between any two adjacent numbers in the machine's floating point system. This number is obviously system-dependent. On machines that support 64 bit IEEE floating point arithmetic, eps is approximately 2.2204e-16.

— Built-in Variable: realmax

The largest floating point number that is representable. The actual value is system-dependent. On machines that support 64-bit IEEE floating point arithmetic, realmax is approximately 1.7977e+308

— Built-in Variable: realmin

The smallest normalized floating point number that is representable. The actual value is system-dependent. On machines that support 64-bit IEEE floating point arithmetic, realmin is approximately 2.2251e-308