Signum Function

The signum function is a compact way to capture the sign of a real number — whether it is positive, negative, or zero. It is defined piecewise: $f(x) = 1$ for $x > 0$, $f(x) = -1$ for $x < 0$, and $f(0) = 0$. This function is a classic example of a discontinuous function at $x = 0$, making it a perfect tool for understanding limits and one-sided behaviour. You will often see it used to model switching phenomena or …