$$y=|$$$$x$$$$|\;=\;$$$$\left\{\begin{matrix} x,\;\;x\geq 0\\ -x,\;\;x<0 \end{matrix}\right.$$
$$y=sign(x)=$$ $$sgn(x)=$$ $$signum(x)=$$$$\left\{\begin{matrix} 1,\;\;x>0\\ -1,\;\;x<0 \end{matrix}\right.$$
$$y=\;[$$$$x$$$$]$$$$\;=k\;\;при\;\;x\in [k,\;k+1)$$
$$y=\{$$$$x$$$$\}\;$$$$=x-[x]$$