ABSTRACT
This is perhaps the most famous of the paradoxes of Zeno of Elea (born c. 490 BC).
Summing an Infinite Series
Of course we know that Achilles will catch the tortoise. He completes the infinitely many intervals in a finite time because each successive interval, being smaller than the one before, is crossed more quickly than its predecessor. Suppose Achilles catches the tortoise after running a mile. The infinitely many smaller and smaller intervals he traverses have to add up to a mile. But how can that be?
