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The Factoradic Integers

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dc.contributor.authorBrinsfield, Joshua Solen
dc.contributor.committeechairFloyd, William J.en
dc.contributor.committeememberMihalcea, Constantin Leonardoen
dc.contributor.committeememberBrown, Ezra A.en
dc.contributor.departmentMathematicsen
dc.date.accessioned2016-06-25T08:00:46Zen
dc.date.available2016-06-25T08:00:46Zen
dc.date.issued2016-06-24en
dc.description.abstractThe arithmetic progressions under addition and composition satisfy the usual rules of arithmetic with a modified distributive law. The basic algebra of such mathematical structures is examined; this leads to the consideration of the integers as a metric space under the "factoradic metric", i.e., the integers equipped with a distance function defined by d(n,m)=1/N!, where N is the largest positive integer such that N! divides n-m. Via the process of metric completion, the integers are then extended to a larger set of numbers, the factoradic integers. The properties of the factoradic integers are developed in detail, with particular attention to prime factorization, exponentiation, infinite series, and continuous functions, as well as to polynomials and their extensions. The structure of the factoradic integers is highly dependent upon the distribution of the prime numbers and relates to various topics in algebra, number theory, and non-standard analysis.en
dc.description.degreeMaster of Scienceen
dc.format.mediumETDen
dc.identifier.othervt_gsexam:8460en
dc.identifier.urihttp://hdl.handle.net/10919/71451en
dc.publisherVirginia Techen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectDistributive Lawen
dc.subjectArithmetic Progressionen
dc.subjectP-adic Numberen
dc.subjectFactorialen
dc.titleThe Factoradic Integersen
dc.typeThesisen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.levelmastersen
thesis.degree.nameMaster of Scienceen

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