The Sign function reference article from the English Wikipedia on 24-Apr-2004 (provided by Fixed Reference: snapshots of Wikipedia from wikipedia.org)

Sign function

In mathematics and especially in computer science, the sign function is a logical function which extracts the sign of a real number. To avoid confusion with the sine function, this function is often called the signum function. The sign function is often represented as sgn and can be defined thus:

Any real number can be expressed as the product of its absolute value and its sign function:

.

From equation (1) it follows that

but equation (2) is indeterminate when x is set to zero.

The signum function is the derivative of the absolute value function (up to the indeterminacy at zero):

Also, the derivative of the signum function is two times the Dirac delta function,

The signum function is related to the Heaviside step function h_0.5(x) thus

where the 0.5 subscript of the step function means that

Also, if the step function u₀(x) is thought of as a mathematical switch, with then the signum function can be expressed as

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