1. The problem statement, all variables and given/known data Prove that if a>0, there exists n in N such that 1/n < a < n. 2. Relevant equations 3. The attempt at a solution I am starting with a>0 and trying to manipulate, algebraically, to get n > a > 1/n. From a > 0 I can add 1 to both sides to obtain, a+1 > 1. Then I can choose some n such that: n > a+1 > 1. From there, divide by n to achieve the desired result for one part of the inequality: 1> (a+1)/n > 1/n. We know from above that n > 1, so I can write: n > (a+1)/n > 1/n. From here I'm not sure what to do.