Solved cryptogram
The fractions can be put in a single numbered list, even though they never run out.
Mathematics Facts, sourced to Wolfram MathWorld.
Solve it yourself
This fact is a cryptogram here: 66 letters over 20 different ones, graded hard.
Or go to the puzzle’s own page first.
What it means
This is the surprise that sits beside Cantor's other result. Between any two fractions there is another one, so they are packed infinitely tightly on the line, and yet they can be arranged in a sequence with a first, a second and a third. The trick is to sort them by the sum of the top and bottom numbers rather than by size. So the fractions and the counting numbers are the same size of infinity, and the decimals are not.
The claim comes from Wolfram MathWorld.
- SourceWolfram MathWorld
- CollectionMathematics Facts
- Difficultyhard
- Length66 letters, 20 of them different
Nearby in the collection
The facts either side of this one.
- Wolfram MathWorldeasy, 77 letters
- Wolfram MathWorldmedium, 72 letters
- Wolfram MathWorldmedium, 70 letters
- Wolfram MathWorldhard, 72 letters
About as hard as this one
Scored closest to it by the model behind our guide to solving cryptograms.
- Wolfram MathWorldhard, 74 letters
- MacTutor History of Mathematicshard, 69 letters
- Wolfram MathWorldhard, 74 letters
- Wolfram MathWorldhard, 75 letters