Solved cryptogram
Some infinities are bigger than others. There are more real numbers than whole numbers.
Mathematics Facts, sourced to Wolfram MathWorld.
Solve it yourself
This fact is a cryptogram here: 72 letters over 16 different ones, graded medium.
Or go to the puzzle’s own page first.
What it means
Cantor's argument is short enough to follow. Suppose you had a list pairing every whole number with every decimal between zero and one. Build a new decimal whose first place differs from the first entry on the list, whose second place differs from the second, and so on. The result differs from every line of the list somewhere, so it was not on it, and the list was never complete. No pairing can work, and one infinity is strictly larger.
The claim comes from Wolfram MathWorld.
- SourceWolfram MathWorld
- CollectionMathematics Facts
- Difficultymedium
- Length72 letters, 16 of them different
Nearby in the collection
The facts either side of this one.
- Wolfram MathWorldeasy, 71 letters
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- Wolfram MathWorldhard, 66 letters
- Wolfram MathWorldmedium, 70 letters
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