 This paradox turns on much the same considerations as the last. Imagine Achilles chasing a tortoise, and suppose that Achilles is running at 1 m/s, that the tortoise is crawling at 0.1 m/s and that the tortoise starts out 0.9m ahead of Achilles. On the face of it Achilles should catch the tortoise after 1s, at a distance of 1m from where he starts (and so 0.1m from where the Tortoise starts). We could break Achilles’ motion up as we did Atalanta’s, into halves, or we could do it as follows: before Achilles can catch the tortoise he must reach the point where the tortoise started. But in the time he takes to do this the tortoise crawls a little further forward. So next Achilles must reach this new point. But in the time it takes Achilles to achieve this the tortoise crawls forward a tiny bit further. And so on to infinity: every time that Achilles reaches the place where the tortoise was, the tortoise has had enough time to get a little bit further, and so Achilles has another run to make, and so Achilles has an infinite number of finite catch-ups to do before he can catch the tortoise, and so, Zeno concludes, he never catches the tortoise.