1. The problem statement, all variables and given/known data I need to prove that a closed ball(radius r about x0) is closed and bounded. The same goes for a sphere(radius r about x0). 2. Relevant equations 3. The attempt at a solution How does one go about proving something is closed and bounded? My book is not very helpful and searching hasn't yielded much. This is only a part of the problem, but the rest should be doable once I get this.