1. The problem statement, all variables and given/known data The relation R, on the set ℝxℝ, is defined by (x,y)R(a,b) if and only if x+b=a+y for any real number x,y,a, and b. Let G denote the set of equivalence classes of the relation R. Question: Let f: ℝ -> G be defined by f(a)=[(0,a)]. Prove that f is a bijection. 3. The attempt at a solution I think I have to come up with an equation, for f(a)=[(0,a)]. I also think I could prove this using induction. I am very confused and need a leg up on how to start! Any help would be greatly appreciated.