Which description represents the Achilles and the tortoise paradox?

Which description represents the Achilles and the tortoise paradox?

• A. The finish line is never reached because time is infinite.
• B. The tortoise will always stay ahead since it is faster.
• C. Achilles cannot overtake the tortoise because he must first reach every point where the tortoise previously was.
• D. The paradox proves motion cannot occur in a finite sequence of points.

Answer: (C)

Zeno’s Achilles and the tortoise is built on the idea that to catch up, Achilles would have to reach every point the tortoise has already occupied. That description matches the paradox because it frames motion as an infinite sequence of ever-smaller tasks: each time Achilles reaches the tortoise’s previous position, the tortoise has moved a bit farther, creating another point Achilles must reach, and so on. The paradox hinges on thinking there are infinitely many such points, which would take an infinite amount of time, yet in reality the total time adds up to a finite amount because the distances shrink in each step. This is where the idea of limits and convergent sums resolves the puzzle. The other descriptions miss the setup: the finish line not being reached in infinite time misstates the focus on an endless sequence of points; the tortoise always staying ahead ignores the catch-up scenario the paradox is about; and claiming motion cannot occur in a finite sequence of points contradicts the very premise of a continuous motion being described by an infinite subdivision.

Zeno’s Achilles and the tortoise is built on the idea that to catch up, Achilles would have to reach every point the tortoise has already occupied. That description matches the paradox because it frames motion as an infinite sequence of ever-smaller tasks: each time Achilles reaches the tortoise’s previous position, the tortoise has moved a bit farther, creating another point Achilles must reach, and so on. The paradox hinges on thinking there are infinitely many such points, which would take an infinite amount of time, yet in reality the total time adds up to a finite amount because the distances shrink in each step. This is where the idea of limits and convergent sums resolves the puzzle.

The other descriptions miss the setup: the finish line not being reached in infinite time misstates the focus on an endless sequence of points; the tortoise always staying ahead ignores the catch-up scenario the paradox is about; and claiming motion cannot occur in a finite sequence of points contradicts the very premise of a continuous motion being described by an infinite subdivision.