Absolute Value Function

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An Absolute Value Function of any real number is always its positive value

[math]|x| =\left\{\begin{array}{ll}x \quad\textrm{for} \quad x \geq 0\\-x \quad\textrm{for}\quad x \lt 0\end{array}\right.[/math]
  • Example(s):
    • |-3|=3
    • [math]|(3,0,4)|=\sqrt{3^2+0^2+4^2}=5[/math]
    • [math] |3+i4|=\sqrt{3^2+4^2}=5 [/math]
  • Counter-Example(s):

See: Numeric Function, Positive Value, Negative Value, Complex Number Modulus.



References

2016

[math]|x|=xsgn(x)[/math]
where sgn(x) is the sign function. The absolute value is therefore always greater than or equal to 0. (...) The absolute value of a complex number [math]z=x+iy[/math], also called the complex modulus,

2008