Cantor’s diagonal
For each number on the list, change the highlighted digit. The number you build won’t be anywhere on the list.
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Try the experiment: your result will appear here, next to what most people do.
What just happened (read it after the experiment)
The number you build differs from the first on the list in its first decimal place, from the second in its second, and so on: it can’t be anywhere on the list. No list, even an infinite one, contains all the numbers between 0 and 1.
Georg Cantor published this argument in 1891. He concluded that there are strictly more real numbers than whole numbers: infinity comes in several sizes.
The discovery brought him ridicule and hostility; today it lies at the heart of mathematics.
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Sources
- Georg Cantor, “Über eine elementare Frage der Mannigfaltigkeitslehre,” 1891.