What does $f(\cdot)$ mean in math Let $f:\mathbb{R} \to \mathbb{R}$ be a function, what does $f(\cdot)$ mean usually? Is it another way of writing this function, or is it a real number?

It is another way of writing the function, emphasising that the value of $f$ at, for instance, $5$ is written as $f(5)$, and not $f5$ or $5f$ or $(5)f$ or $f|_5$ or anything else. The dot is just a placeholder.
Some would write this as $f(x)$ instead of $f(\cdot)$, but this is a slightly different emphasis again. The notation $f(x)$ tends to be associated to a specific description of $f$, for instance $f(x) = 4x-3$.
