Which paradox is described as crossing half the remaining distance indefinitely?

Which paradox is described as crossing half the remaining distance indefinitely?

• A. Arrow paradox
• B. Stadium paradox
• C. Dichotomy paradox
• D. Achilles paradox

Answer: (C)

This is about infinite subdivision of a distance and how a finite journey can come from an infinite sequence of ever-smaller steps. You’d first cover half the total distance, then half of what remains, then half of what’s left, and so on. The distances you travel form a geometric series: D/2, D/4, D/8, …, which sums to the full distance D. If speed is constant, the times for each step form a convergent series, so the total time is finite and you reach the destination. The remaining distance after n steps is D·(1/2)^n, which tends to zero as n grows without bound. This is the dichotomy paradox. The other options describe different Zeno setups that aren’t about repeatedly halving the remaining distance.

This is about infinite subdivision of a distance and how a finite journey can come from an infinite sequence of ever-smaller steps. You’d first cover half the total distance, then half of what remains, then half of what’s left, and so on. The distances you travel form a geometric series: D/2, D/4, D/8, …, which sums to the full distance D. If speed is constant, the times for each step form a convergent series, so the total time is finite and you reach the destination. The remaining distance after n steps is D·(1/2)^n, which tends to zero as n grows without bound. This is the dichotomy paradox. The other options describe different Zeno setups that aren’t about repeatedly halving the remaining distance.