Which paradox is described by crossing half the distance first, then half of what remains, and so on?

Which paradox is described by crossing half the distance first, then half of what remains, and so on?

• A. The paradox about infinite subdivision of distance
• B. The arrow paradox
• C. The stadium paradox
• D. The rational decision paradox

Answer: (B)

This describes Zeno’s dichotomy paradox, the idea that motion seems impossible because you must complete an infinite sequence of steps. To reach a point you first cover half the distance, then half of what remains, then half again, and so on. Those steps form a geometric series with halves: 1/2, 1/4, 1/8, and so forth. Although there are infinitely many steps, the total distance you must travel adds up to the whole distance because the infinite sum converges. If each step takes time proportional to the distance covered, the total time is also finite, so you can arrive despite the infinite subdivision. The arrow paradox, by contrast, looks at motion through instantaneous snapshots and argues the object is at rest at each instant, not about halving distances; that’s a different toy example in Zeno’s repertoire. The described scenario is the paradox about infinite subdivision of distance.

This describes Zeno’s dichotomy paradox, the idea that motion seems impossible because you must complete an infinite sequence of steps. To reach a point you first cover half the distance, then half of what remains, then half again, and so on. Those steps form a geometric series with halves: 1/2, 1/4, 1/8, and so forth. Although there are infinitely many steps, the total distance you must travel adds up to the whole distance because the infinite sum converges. If each step takes time proportional to the distance covered, the total time is also finite, so you can arrive despite the infinite subdivision. The arrow paradox, by contrast, looks at motion through instantaneous snapshots and argues the object is at rest at each instant, not about halving distances; that’s a different toy example in Zeno’s repertoire. The described scenario is the paradox about infinite subdivision of distance.