1. The problem statement, all variables and given/known data Show that any rational in the interval (0,1] can be expressed as a finite sum r=1/q1+1/q2+...+1/qn where the qj are integers and q1<q2<...<qn. 2. Relevant equations 3. The attempt at a solution Let x[itex]\in[/itex]Q and 0<x[itex]\leq[/itex]1. Prove [itex]\exists[/itex]q1, q2, ..., qn[itex]\in[/itex]N with q1<q2<...<qn. My professor suggests using the greedy algorithm but I don't understand how that would help the proof.