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

## DSpace/Manakin Repository

 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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