The arrow paradox

A second version of the paradox (called the dichotomy) concerns an arrow that must reach a target.

History — The arrow paradox (dichotomy)

To reach the target at distance $L$, the arrow must first cover $L/2$, then $L/4$, then $L/8$, and so on to infinity. It therefore seems that it can never arrive.

Here too the sum of infinitely many pieces is a geometric series that converges to a finite value:

$\frac{L}{2} + \frac{L}{4} + \frac{L}{8} + \cdots = L.$

The finite is the sum of infinitely many pieces: the arrow reaches the target, and the mathematics of the limit confirms it.

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Topics: Limits
Concepts: Limit · Geometric series
People: Zeno