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Complete Ordered Fields

The purpose of this thesis is to study the concept of completeness in an ordered field. Several conditions which are necessary and sufficient for completeness in an ordered field are examined. In Chapter I the definitions of a field and an ordered field are presented and several properties of fields and ordered fields are noted. Chapter II defines an Archimedean field and presents several conditions equivalent to the Archimedean property. Definitions of a complete ordered field (in terms of a least upper bound) and the set of real numbers are also stated. Chapter III presents eight conditions which are equivalent to completeness in an ordered field. These conditions include the concepts of nested intervals, Dedekind cuts, bounded monotonic sequences, convergent subsequences, open coverings, cluster points, Cauchy sequences, and continuous functions.

Identiferoai:union.ndltd.org:unt.edu/info:ark/67531/metadc504449
Date08 1900
CreatorsArnold, Thompson Sharon
ContributorsParrish, Herbert C., Vaughan, Nick H.
PublisherNorth Texas State University
Source SetsUniversity of North Texas
LanguageEnglish
Detected LanguageEnglish
TypeThesis or Dissertation
Formativ, 73 leaves: ill., Text
RightsPublic, Arnold, Thompson Sharon, Copyright, Copyright is held by the author, unless otherwise noted. All rights reserved.

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