Be $\Bbb P\Bbb Q$ the set of all fractions $f_{m,n}=\frac{p_m}{p_n}$ whose numerador and denominator are both prime numbers.
i) Show that for any open set $A\subset \Bbb R^+$, there is at least one fraction $f \in \Bbb P\Bbb Q$ such that $f \in A$
ii) Show that there are infinitely many elements of $\Bbb P\Bbb Q$ that belong to any open set $A\subset \Bbb R^+$