Zeno of Elea lived in the 5th century BCE and is remembered for a set of arguments that seem to prove that motion cannot happen.
Achilles and the tortoise
Achilles races a tortoise that starts ahead. By the time Achilles reaches the tortoise's starting point, it has moved on a little. When he reaches that new point, it has moved again. Zeno argued that Achilles must complete infinitely many steps — and so can never catch up.
The dichotomy
To cross a room you must first reach the halfway point, then half of the remaining distance, and so on forever. How can anyone finish infinitely many tasks?
The modern answer
Mathematics shows that an infinite number of steps can add up to a finite total. The series 1/2 + 1/4 + 1/8 + … gets ever closer to 1 and its sum is exactly 1. Infinitely many shrinking distances can be covered in a finite time.
