lean_workbook_plus_80616

Let $x_1, x_2, \ldots , x_k$ be arbitrary reals. Let $\epsilon > 0$ be given. Then there exists a positive integer $n$ and integers $m_1,m_2, \ldots , m_k$ such that $|nx_i - m_i| < \epsilon$ for all $1 \le i \le m$.