Let
be the set of real numbers of the form
, where
and
are positive integers. Prove that for every pair
with
, there exists an element
such that
%V0
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 $x < y$, there exists an element $z \in M$ such that $x < z < y.$
Školjka