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Sgn

\begin{figure}\begin{center}\BoxedEPSF{Sgn.epsf scaled 700}\end{center}\end{figure}

Also called Signum. It can be defined as

\begin{displaymath}
\mathop{\rm sgn}\nolimits \equiv \cases{
-1 & $x < 0$\cr
0 & $x = 0$\cr
1 & $x > 0$\cr}
\end{displaymath} (1)

or
\begin{displaymath}
\mathop{\rm sgn}\nolimits (x) = 2H(x)-1,
\end{displaymath} (2)

where $H(x)$ is the Heaviside Step Function. For $x\not=0$, this can be written
\begin{displaymath}
\mathop{\rm sgn}\nolimits (x) \equiv {x\over\vert x\vert}.
\end{displaymath} (3)

See also Heaviside Step Function, Ramp Function




© 1996-9 Eric W. Weisstein
1999-05-26