Give a tortoise a head start, and Achilles can logically never catch it

Zeno of Elea argued that fast Achilles, racing a slow tortoise given a head start, can never overtake it: by the time he reaches where the tortoise was, it has always moved a little further ahead, forever. Each gap takes some finite time to close, and there are infinitely many gaps, so logic seems to demand an infinite chase. Calculus eventually showed an infinite series of shrinking intervals can still sum to a finite total, but the paradox still unsettles intuitions about infinity.

— Zeno of Elea, Zeno's paradoxes — 5th century BC, preserved in Aristotle's Physics