::That premise could then be extended to any action that occurs over a period of time. And, because we (and Zeno) treat space much like we treat time, it would mean any length has neither a beginning nor an end. The first and last intervals could always be divided further. Together, this would essentially imply that continuous time and space, in-and-of themselves, are paradoxical, because no amount of time, nor any length, could be complete. At this point, it may be more a question of what it means to divide by infinity than anything else, because you simply can't divide by infinity and expect a number that has an end (although 0.999... is considered equal to 1, but I don't know if you can extend this to 0.000...1 = 0). Dividing anything by infinity simply leaves no beginning nor end. If time (or space) were discrete, however, there would always be a first and a final step, because there would be a indivisible amount of time (or space) that could start or end, because you couldn't divide it further. The premise you highlighted would still stand; it just wouldn't be relevant.