Math Beauties in need of HELP!!!! 1. The problem statement, all variables and given/known data the question is....why the set of irrational numbers is not an open subset of Real numbers? 2. Relevant equations none that i am aware of 3. The attempt at a solution can we say that..... assume that the irrational numbers are open. but we know that the set of real numbers is infinite and much larger than the set of irrational numbers. therefore, there is not a one to one mapping of irrational numbers to rational numbers. Please help us. we are so lost. it would be greatly appreciated.