Question 16
(GDR 4) Prove the following statement: If $r_1$ and $r_2$ are real numbers whose quotient is irrational, then any real number $x$ can be approximated arbitrarily well by numbers of the form $z_{k_1,k_2}=k_1r_1+k_2r_2$, $k_1,k_2$ integers; i.e., for every real number $x$ and every positive real number $p$ two integers $k_1$ and $k_2$ can be found such that $|x-(k_1r_1+k_2r_2)|\lt p$.