Achilles races a tortoise with a head start — logically, can he ever catch it?
Give the tortoise a head start in a race against Achilles, the fastest runner in Greek legend. Zeno argued that by the time Achilles reaches the tortoise's starting point, it has moved a little further ahead; by the time he closes that new gap, it has moved again, and so on forever. If each gap must be closed in sequence, does Achilles ever actually catch the tortoise?
Reveal the answer
Achilles does catch the tortoise, and in finite time: the gaps shrink so fast that infinitely many of them still sum to a finite distance and duration, a fact only rigorously established millennia later with the mathematics of convergent infinite series. Aristotle recorded this, the most famous of Zeno's motion paradoxes, in his Physics around 350 BCE.
— Aristotle, recording Zeno of Elea's paradox, Physics — Book VI, c. 350 BCE