1. The problem statement, all variables and given/known data If x and y are arbitrary real numbers with x<y, prove that there is at least one real z satisfying x<z<y 2. Relevant equations 3. The attempt at a solution The problem arises from my inexperience in rigorously proving anything. If possible a general explanation of where to begin when trying to prove something rigorously would be more helpful than just the answer. I find that proofs generally seem obvious after i see them completed, but i sit for hours staring at them not knowing where to even remotely begin. Any help would be greatly appreciated. Thanks!