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Mathematics

The Diagonalization Argument and Its Use in Proving Uncountability

Quick fact

The diagonalization argument proves that the set of real numbers is uncountable by constructing a number that cannot appear anywhere on any proposed list, no matter how the list is arranged.

Why this is interesting

You know there are infinitely many numbers, but are all infinite sets the same size? The diagonalization argument shows that some infinities are larger than others—prepare to have your intuition stretched.