RU-ALLRUSSIAN 1978 Problem 6

Show that there is an infinite sequence of reals $\mathrm{x}_{1}$ , $\mathrm{x}_{2}$ , $\mathrm{x}_{3}$ , ... such that $\mathrm{l}\mathrm{x}_{\mathrm{n}}\mathrm{l}$ is bounded and for any $\mathrm{m} > \mathrm{n}$ , we have $\mathrm{l}\mathrm{x}_{\mathrm{m}} - \mathrm{x}_{\mathrm{n}}\mathrm{l} > 1 / (\mathrm{m} - \mathrm{n})$ .