The Pendulum Problem

I was watching a film in my oceanography class about waves when I started to think about the energy loss and motion of pendulums. I want to know if a pendulum in a vacuum will ever stop moving completely. I know there is friction within the pendulum. I also know that the distance that the bob travels in each swing decreases multiplicatively. In calculus I learned that multiplying something by a number n such that 0<n<1 infinitely many times approaches 0. Does this apply to the pendulum's velocity?

Does a pendulum actually stop moving completely or does it seem to stop but still move?