Mathematics I / Number Theory in Action
Practice question · Multiple choice

Zeno argued you can never cross a room: first half the distance, then half the rest, forever. Why does the mathematics of series dissolve the paradox?

Hints
  1. Write down the time for each half-step. Now add them.
  2. The number of steps is infinite. Ask whether that forces the total to be.
Show the answer

C. Because the times form a convergent series with a finite total

Why

The steps shrink fast enough that the times sum to a finite number: infinitely many additions with a finite total. Zeno's error was assuming an infinite count of intervals means infinite duration, and the resolution had to wait about two thousand years for the definition of a convergent series.

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