Sign Function: Different Representation?

[bomba923]

For example, the function
$$f\left( x \right) = \left\{ {\begin{array}{*{20}c} {1:x > 0} \\ {0:x = 0} \\ { - 1:x < 0} \\ \end{array} } \right.$$
is known as the sign function, usually represented as sgn x.

However, is there a specific name for the function
$$f\left( x \right) = \left\{ {\begin{array}{*{20}c} {1:x > 0} \\ { - 1:x \leqslant 0} \\ \end{array} } \right.$$
?

 

[quasar987]

I would simply say that it is a step function. One of the step functions has a name: http://en.wikipedia.org/wiki/Heaviside_step_function

 

[bomba923]

Well, in that case, my function is simply 2H₀(x)-1

 

[mathwonk]

the name of the function is yahweh.