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    Absolutely Normal

    Definition

    A real number that is b-normal for every base 2, 3, 4, ... is said to be absolutely normal. As proved by Borel, almost all real numbers in [0, 1) are absolutely normal. The first specific construction of an absolutely normal number was by Sierpiński, with another method presented by Schmidt. These results were both obtained by complex constructive devices, and are by no means easy to construct (Stoneham 1970, Sierpiński and Schinzel 1988).

    Related term

    normal number

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