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

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dc.contributor.advisor Burton Jr, Robert M.
dc.creator Rockwell, Daniel Luke
dc.date.accessioned 2011-09-22T19:36:59Z
dc.date.available 2011-09-22T19:36:59Z
dc.date.copyright 2011-09-09
dc.date.issued 2011-09-09
dc.identifier.uri http://hdl.handle.net/1957/23486
dc.description Graduation date: 2012 en_US
dc.description.abstract The notion of a normal number and the Normal Number Theorem date back over 100 years. Émile 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. en_US
dc.language.iso en_US en_US
dc.subject normal number en_US
dc.subject symbolic dynamical systems en_US
dc.subject Fibonacci substitution en_US
dc.subject Fibonacci word en_US
dc.subject Sturmian en_US
dc.subject.lcsh Normal numbers en_US
dc.subject.lcsh Fibonacci numbers en_US
dc.title A reinterpretation, and new demonstrations of, the Borel Normal Number Theorem en_US
dc.type Thesis/Dissertation en_US
dc.degree.name Doctor of Philosophy (Ph. D.) in Mathematics en_US
dc.degree.level Doctoral en_US
dc.degree.discipline Science en_US
dc.degree.grantor Oregon State University en_US
dc.contributor.committeemember Garity, Dennis
dc.contributor.committeemember Swisher, Holly
dc.contributor.committeemember Kevchegov, Yevgeniy
dc.contributor.committeemember Rorrer, Greg
dc.description.peerreview no en_us

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