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On normal numbers

Published online by Cambridge University Press:  09 April 2009

C. E. M. Pearce  and
M. S. Keane
C. E. M. Pearce
Affiliation:
University of Adelaide, Adelaide, Australia
M. S. Keane
Affiliation:
Université de Rennes, Rennes, France
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Abstract

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Schmidt has shown that if r and s are positive integers and there is no positive integer power of r which is also a positive integer power of s, then there exists an uncountable set of reals which are normal to base r but not even simply normal to base s. We give a structurally simple proof of this result

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 32 , Issue 1 , January 1982 , pp. 79 - 87
Copyright
Copyright © Australian Mathematical Society 1982

References

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