Let $X$ be a set of rational numbers satisfying the following two conditions: (a) The set $X$ contains at least two elements, (b) For any $x, y$ in $X$, if $x \ne y$ then there exists $z$ in $X$ such that either $\left| \frac{x- z}{y - z} \right|= 2$ or $\left| \frac{y -z}{x - z} \right|= 2$ . Prove that $X$ contains infinitely many elements.