Solved cryptogram

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

Mathematics Facts, sourced to Wolfram MathWorld.

Solve it yourself

This fact is a cryptogram here: 72 letters over 20 different ones, graded hard.

Or go to the puzzle’s own page first.

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.

About as hard as this one

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

Play a cryptogram

Every Mathematics Facts cryptogram · All fact collections