Almost All Real Numbers are Normal

Theorem

Almost all real numbers are normal.


Proof


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Historical Note

That was proved in $1909$ by Émile Borel.


Sources

  • 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Champernowne's number
  • 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): normal number
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