Sign (mathematics)

The sign of a real number indicates whether it is positive, negative, or zero. Sign also describes the direction of a nonzero quantity relative to zero.

Positive number: A real number greater than zero. A positive sign identifies numbers greater than zero.
Sign chart: A table showing where an expression is positive, negative, or zero across intervals. Sign charts track changes in sign across roots and discontinuities.
Discriminant: An expression in a polynomial's coefficients that reveals properties such as the nature of its roots. Its sign distinguishes the real-root cases of a quadratic equation.
Magnitude: The size of a quantity, considered without its direction or sign. Magnitude captures size, whereas sign distinguishes positive from negative.
Negative number: A real number less than zero. A negative sign identifies numbers less than zero.
Multiplication of signed numbers: Rules determining the sign of a product from the signs of its factors. A product is positive for like signs and negative for unlike signs.
Definite integral: A number representing the signed accumulation of a function over an interval. Regions below the horizontal axis contribute negative rather than positive area.
Complex number: A number expressible as a real part plus an imaginary part. Complex numbers do not have the ordinary positive-or-negative ordering of real numbers.
Zero: The additive identity, separating positive real numbers from negative real numbers. Zero is neither positive nor negative and forms the boundary between the two signs.
Signum function: The function assigning −1, 0, or 1 according as a real input is negative, zero, or positive. It encodes sign as a numerical output.

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Sign functionRelated: The function encodes this three-way classification as a numerical output.