1. The problem statement, all variables and given/known data Prove that there exists an irrational between any two rationals. 2. Relevant equations 3. The attempt at a solution How would one do this? So far I've proven there is an irrational between any rational and irrational, any irrational and rational, that there's a rational between any two reals, or a irrational between any two reals in the attempt; I realize that it can be taken as a case of the last two; but I haven't been able to start with just p,q such that p>q, and p and q rational, and arrive at this result. It's pissing me off. Thanks in advance.