SE-SKOLORNAS 1966 Problem 1

Let $\{x\}$ denote the fractional part of $x$ , $x - [x]$ . The sequences $x_1, x_2, x_3, ...$ and $y_1, y_2, y_3, ...$ are such that $\lim \{x_n\} = \lim \{y_n\} = 0$ . Is it true that $\lim \{x_n + y_n\} = 0$ ? $\lim \{x_n - y_n\} = 0$ ?