1. The problem statement, all variables and given/known data Given any real x > 0, prove that there is an irrational number between 0 and x. 2. Relevant equations I'm not sure if the concepts of supremums or upper bounds can used. 3. The attempt at a solution Take an irrational number say Pi. We can always choose a number n such that n*Pi is between 0 and x. Thus for every real x > 0, there is at least one irrational number between 0 and x. Is this correct? If so, what other methods are there?