Achilles can never catch the tortoise. Motion is impossible. He invented the paradox as a philosophical weapon.
Zeno was Parmenides' student and defender. When critics mocked the idea that change is impossible, Zeno answered not with theories but with puzzles. If Achilles gives a tortoise a head start, he can never catch it, because he must first reach where the tortoise was, by which time it has moved on. An arrow in flight is at rest at every instant, so it never moves. These paradoxes were not riddles. They were arguments designed to show that the critics' own assumptions about space, time, and motion led to absurdity.
“If everything that exists has a place, place too will have a place, and so on to infinity.”
Invented a series of arguments designed to show that motion and plurality are logically impossible, defending his teacher Parmenides against critics.