 Although it has infinitely many terms, this sum is a geometric series that converges to 1 in the standard topology of the real numbers. A discussion of the philosophy underpinning this fact can be found in Salmon (1998), and the mathematics of convergence in any real analysis textbook that deals with infinite series. From this perspective, Achilles actually does complete all of the supertask steps in the limit as the number of steps goes to infinity. One might only doubt whether or not the standard topology of the real numbers provides the appropriate notion of convergence in this supertask. A discussion of the subtleties of the choice of topology has been given by Mclaughlin (1998).