Sign function
The sign function maps each real number to −1, 0, or 1 according to whether it is negative, zero, or positive.
Piecewise function: A function defined by different formulas on different parts of its domain. The sign function uses separate constant values for negative, zero, and positive inputs.
Real number: An element of the complete ordered field represented by the real number system. The sign function’s stated domain is the real numbers.
Sign error: The discrepancy between a computed sign and the correct sign of a quantity. Sign checks use the function to encode whether a numerical result is positive or negative.
Signum function: A name commonly used for the real sign function, with conventions that can vary at zero. It is often synonymous with this function, but some definitions assign a different value at zero.
Absolute value: A real number’s nonnegative distance from zero, denoted by vertical bars. For nonzero inputs, the sign function equals the input divided by its absolute value.
Positive number: A real number greater than zero. Positive inputs are exactly those assigned the value one.
Sign test: A nonparametric statistical test based on the signs of paired differences or deviations. It reduces observations to positive, negative, or zero signs.
Absolute sign: The notation of vertical bars used to denote absolute value or related operations. Despite its name, the sign function returns polarity, while absolute value returns magnitude.
Indicator function: A function that equals one when a condition holds and zero otherwise. The sign function can be expressed using indicators of the positive and negative half-lines.
Negative number: A real number less than zero. Negative inputs are exactly those assigned the value minus one.