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!

It's called the Sign function, also called the Signum function:
$$\large \text{sgn}(x) = 
\begin{cases} \frac{d}{dx} \left| x\right| =  \frac{x}{\left| x\right|} , \text{when } x \neq0\\
0\space, \text{when} \space x=0
\end{cases} $$
 $\leftarrow$ It is clearly a piecewise step function.
