In this well-known paradox, the Greek warrior Achilleus—whom the poet Homer always calls "swift-footed Achilles"—must race against the slowest runner imaginable—namely, a tortoise. If only the tortoise is allowed the slightest head-start, the Parmenidean logician Zeno is prepared to prove that Achilles can never overtake it. Aristotle (384-322 BCE) reports it as follows:

The so-called "Achilles" paradox claims that the fastest can never overtake the slowest runner in a race, since the runner who comes from behind must first reach the point where the front runner started, and so the slower one always holds a lead.

This is essentially the same argument as in the paradox of the "flying" arrow stuck forever in infinitely divisible space, but here it is used with reference to two things moving in relation to each other.

Another paradox, reported by Aristotle:

If ‘place’ exists, where exactly is it? After all, everything that exists, exists in some ‘place.’ As a result, ‘place’ too is in a ‘place.’ This goes on to infinity; and so ‘place’ does not exist.