Achilles and the Tortoise
The Paradox: In this thought experiment, Achilles, a swift warrior, is racing against a slow-moving tortoise. To make it fair, the tortoise is given a head start. The paradox argues that Achilles can never overtake the tortoise, no matter how fast he runs. Here’s how the paradox is laid out: Initial Position : The tortoise starts ahead of Achilles. Achilles Moves to the Tortoise's Initial Position : By the time Achilles reaches the point where the tortoise started, the tortoise has moved forward a small distance. Achilles Moves to the Tortoise's New Position : Achilles then moves to the new position of the tortoise, but by the time he gets there, the tortoise has moved even further ahead. Repetition : This process continues indefinitely, with Achilles always reaching where the tortoise was, but the tortoise always being a little bit ahead. The paradox suggests that Achilles will never be able to overtake the tortoise because there are infinitely many points he must reach where ...
