Abstract
Paper 21: Francisco J. Aragon Artacho, David H. Bailey, Jonathan M. Borwein and Peter B. Borwein, “Walking on real numbers,” Mathematical Intelligencer, vol. 35 (2013), p. 42–60. With permission of Springer.
Synopsis: As mentioned earlier, an age-old question (one that has been the motivation for both ancient and computer-age computations of π and other constants) is that of whether (and why) these digits are “random,” which is usually taken to be the property of normality: a number α is said to be b-normal if every m-long string in the base-b expansion of α appears, in the limit, with frequency precisely 1/b m . It is straightforward to show, using probability and/or measure theory, that almost all real numbers must be normal, but it has been very difficult to prove normality for any of the classical constants of mathematics.
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Artacho, F.J.A., Bailey, D.H., Borwein, J.M., Borwein, P.B. (2016). Walking on real numbers (2013). In: Pi: The Next Generation. Springer, Cham. https://doi.org/10.1007/978-3-319-32377-0_21
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