Suppose that \{a_n\} is a sequence of real numbers and that $L = \lim_{n \to \infty} a_n$. Suppose that $M_1 \le a_n \le M_2$ for all $n$. Prove that $M_1 \le L \le M_2$. (HINT: Suppose, for instance, that $L > M_2$. Make use of the positive number $L - M_2$ to derive a contradiction.)