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

Graduate Thesis Or Dissertation

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Citeable URL: https://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/8s45qc20b

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Attribute Name	Values
Creator	Rockwell, Daniel Luke
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.
License	All rights reserved
Resource Type	Dissertation
Date Available	2011-09-22T19:36:59+00:00
Date Issued	2011-09-09
Degree Level	Doctoral
Degree Name	Doctor of Philosophy (Ph.D.)
Degree Field	Mathematics
Degree Grantor	Oregon State University
Commencement Year	2012
Advisor	Burton, Robert M., Jr.
Committee Member	Kevchegov, Yevgeniy Rorrer, Greg Swisher, Holly Garity, Dennis
Academic Affiliation	Mathematics
Non-Academic Affiliation	Oregon State University. Graduate School
Subject	Fibonacci numbers Normal numbers
Rights Statement	In Copyright
Publisher	Oregon State University
Peer Reviewed	No
Language	English [eng]
Replaces	http://hdl.handle.net/1957/23486

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