Add a half, a quarter, an eighth and onward forever, and the total is exactly one. Not nearly.

What it means

Zeno used this to argue that motion is impossible: to cross a room you must first cross half of it, then half of what is left, endlessly. The resolution is that an unending list of steps can have a finite total, provided the steps shrink fast enough. Halving does. The sum of a geometric series with a ratio below one is a plain division, and here it gives one on the nose rather than something creeping up on it.

The claim comes from Wolfram MathWorld.

Nearby in the collection

The facts either side of this one.

• Wolfram MathWorldmedium, 74 letters
• Wolfram MathWorldmedium, 75 letters
• Wolfram MathWorldeasy, 70 letters
• Wolfram MathWorldhard, 74 letters

About as hard as this one

Scored closest to it by the model behind our guide to solving cryptograms.

• Wolfram MathWorldhard, 69 letters
• Wolfram MathWorldhard, 73 letters
• Wolfram MathWorldhard, 79 letters
• Wolfram MathWorldhard, 72 letters