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A reinterpretation, and new demonstrations of, the Borel Normal Number Theorem

The notion of a normal number and the Normal Number Theorem date back over 100 years. EĢmile Borel first stated his Normal Number Theorem in 1909. Despite their seemingly basic nature, normal numbers are still engaging many mathematicians to this day. In this paper, we provide a reinterpretation of the concept of a normal number. This leads to a new proof of Borel's classic Normal Number Theorem, and also a construction of a set that contains all absolutely normal numbers. We are also able to use the reinterpretation to apply the same definition for a normal number to any point in a symbolic dynamical system. We then provide a proof that the Fibonacci system has all of its points being normal, with respect to our new definition. / Graduation date: 2012

Identiferoai:union.ndltd.org:ORGSU/oai:ir.library.oregonstate.edu:1957/23486
Date09 September 2011
CreatorsRockwell, Daniel Luke
ContributorsBurton Jr, Robert M.
Source SetsOregon State University
Languageen_US
Detected LanguageEnglish
TypeThesis/Dissertation

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