Mathematical
Zeno's Paradoxes
Motion is impossible because you must cross infinite points
Overview
A set of philosophical problems showing the difficulty of thinking about continuous motion and infinite divisibility.
Achilles and the Tortoise: Achilles gives the tortoise a head start. To catch up, Achilles must first reach where the tortoise was, but by then the tortoise has moved. This repeats infinitely, suggesting Achilles can never catch up - yet he obviously does.