 But what the paradox in this form brings out most vividly is the problem of completing a series of actions that has no final member—in this case the infinite series of catch-ups before Achilles reaches the tortoise. But just what is the problem? Perhaps the following: Achilles’ run to the point at which he should reach the tortoise can, it seems, be completely decomposed into the series of catch-ups, none of which take him to the tortoise. Therefore, nowhere in his run does he reach the tortoise after all. But if this is what Zeno had in mind it won’t do. Of course Achilles doesn’t reach the tortoise at any point of the sequence, for every run in the sequence occurs before we expect Achilles to reach it! Thinking in terms of the points that Achilles must reach in his run, 1m does not occur in the sequence 0.9m, 0.99m, 0.999m, …, so of course he never catches the tortoise during that sequence of runs! (And the same situation arises in the Dichotomy: no first distance in the series, so it does not contain Atalanta’s start!) Thus the series of catch-ups does not after all completely decompose the run: the final point—at which Achilles does catch the tortoise—must be added to it. So is there any puzzle? Arguably yes. 