To get the following proof I followed another similar example, but I'm not sure if it's correct. Does this proof properly show existence and uniqueness? Show that if x is a nonzero rational number, then there is a unique rational number y such that xy = 2 Solution: Existence: The nonzero rational number y = 2/x is a solution of xy = 2 because x(2/x) = 2 = x(2/x) - 2 = x - x = 0. Uniqueness: Suppose s is a nonzero rational number such that xs = 2. Then, xy =2 = xy - 2 = 0 and xs = 2 = xs - 2 = 0. Then: xy - 2 = xs - 2 xy = xs y = s This would be a complete proof wouldn't it?