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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 +1 for a positive number (i.e., one with a plus sign "+"). In other words, for real x,

 sgn(x)={-1   for x<0; 0   for x=0; 1   for x>0.
(1)

For real x!=0, this can be written

 sgn(x)=x/(|x|)
(2)

and satisfies

 sgn(x)=sqrt(x)sqrt(1/x).
(3)

sgn(x) for real x can also be defined as

 sgn(x)=2H(x)-1,
(4)

where H(x) is the Heaviside step function.

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

sgn(0) can also be interpreted as an unspecified point on the unit circle in the complex plane (Rich and Jeffrey 1996).


See also

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

Related Wolfram sites

http://functions.wolfram.com/ComplexComponents/Sign/

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References

Bracewell, R. "The Sign Function, sgnx." In The Fourier Transform and Its Applications, 3rd ed. New York: McGraw-Hill, pp. 61-62, 1999.Rich, A. and Jeffrey, D. "Function Evaluation on Branch Cuts." SIGSAM Bull., No. 116, 25-27, June 1996.

Referenced on Wolfram|Alpha

Sign

Cite this as:

Weisstein, Eric W. "Sign." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Sign.html

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