Is there a name for the function that gives me the signal of a number only? I know the function that gives the absolute value of a number is called either absolute function or 'modulus' function, such as:
$$
modulus(-6) = modulus(6) = 6
$$
Now, I want to name a function that gives me a unit value with the same signal as the input number, like this:
$$
function(-6) = -1
$$
$$
function(6) = 1
$$
Then I can do this:
$$
modulus(-6) \times function(-6) = -6
$$
I could just call it signal(x) but I'd like to know if there is a name for this function.
Thank you all very much!

That's that signum function.
Actually:
$$\text{signum}(x)=\begin{cases}\begin{align}1,\quad x>0\\0,\quad x=0\\-1,\quad x<0\end{align}\end{cases}$$
See it at wikipedia or WolframMathworld.
