Question 19
C7 (CZS 3). Let $M$ be the set of real numbers of the form $\frac{m+n}{\sqrt{m^2+n^2}}$, where $m$ and $n$ are positive integers. Prove that for every pair $x\in M,y\in M$ with $x\lt y$, there exists an element $z\in M$ such that $x\lt z\lt y$.