You considered only the case . Also, since the problem is so basic, the proof has to be really detailed, and I am not sure you sufficiently explained why when . So, what happen when ? Recall that by definition is a nonnegative number such that .
You considered only the case . Also, since the problem is so basic, the proof has to be really detailed, and I am not sure you sufficiently explained why when . So, what happen when ? Recall that by definition is a nonnegative number such that .