Reprint: On the decimal expansion of certain irrational numbers (1937)

  • Kurt Mahler


Let denote the base- expansion of the integer . The Champernowne number to the base is the concatenation of the base- expansions of the positive integers after a radix point; that is, the number 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)].