1. The problem statement, all variables and given/known data Let x and y be real numbers with x<y and write an inequality involving a rational number p/q capturing what we need to prove. Multiply everything in your inequality by q, then explain why this means you want q to be large enough so that q(y-x)>1 . Explain how you can rewrite this inequality and use the Archimedean property to find such a q. 3. The attempt at a solution So, this is a question on a worksheet our teacher gave us to go along with the theorem in the book. Here is what I did so far: x < p/q < y Then multiply both sides by q as the question states: qx < p < yq 0 < p-qx < yq-qx 0 < p-qx < q(y-x) I am having trouble seeing why q(y-x)>1. It is obviously great than zero as the inequality states, but can someone help me see why it has to be >1??