Discreet Mathematics Exercises #1

cusp-5.0m . Prove that a number is rational iE its decimal representation becomes periodic. {Repeated [J's is periodic!) . Write the number [LE as a ratio of two integers Write the number 35.? as the ratio of two integers. . Prove that between any two rational numbers there is a rational number. . Prove that between any two rational numbers there is an irrational num ber. . Let at = and an = .g'l + rn_1. Prove that for all to, an is an irrational number. Prove that :3, = nn-- 1}- 5-1