The sign of a real number, also called sgn or signum, is -1 for a negative number (i.e., one with a minus sign ""), 0 for the number zero, or for a positive number (i.e., one with a plus sign ""). In other words, for real x,

For real , this can be written

and satisfies

for real x can also be defined as

where H(x) is the Heaviside step function.

The sign function is implemented in Mathematica for real x as Sign[x]. For nonzero complex numbers, Sign[z] returns , where is the complex modulus of z.

can also be interpreted as an unspecified point on the unit circle in the complex plane (Rich and Jeffrey 1996).

 

Absolute Square, Absolute Value, Complex Modulus, Heaviside Step Function, Imaginary Part, Minus Sign, Negative, Plus Sign, Positive, Ramp Function, Real Part, Sgn, Zero