Question 23
Let $f: \mathbb{R} \to \mathbb{R}$ be a function such that its 2-fold composition is equal to the floor function, i.e. $f(f(x)) = \lfloor x \rfloor$, for any real number $x$. Prove that there exist distinct real numbers $a$ and $b$ such that $|f(a) - f(b)| \ge |a - b|$.