Reprint: On the decimal expansion of certain irrational numbers (1937) (Q1996501)
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scientific article; zbMATH DE number 7317817
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Reprint: On the decimal expansion of certain irrational numbers (1937) |
scientific article; zbMATH DE number 7317817 |
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Reprint: On the decimal expansion of certain irrational numbers (1937) (English)
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5 March 2021
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Summary: Let \((n)_q\) denote the base-\(q\) expansion of the integer \(n\). The Champernowne number to the base \(q\) is the concatenation of the base-\(q\) expansions of the positive integers after a radix point; that is, the number \[0.(1)_q(2)_q(3)_q\cdots(n)_q\cdots. \] In this paper, Mahler shows that each of these numbers is transcendental, but is not a Liouville number. Reprint of the author's paper [Mathematica B, Zutphen 6, 22--36 (1937; Zbl 0018.11102; JFM 63.0155.03)].
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