An Axiomatic Development of the Properties of Real Numbers Through the Use of Set Theory

Author

Elton E. Beougher, Fort Hays Kansas State College

Department

Math

Degree Name

Master of Arts (MA)

Abstract

The purpose of this paper is to present a logical development of the real number system from a few basic assumptions in a form that an undergraduate can use. The development is based on properties of sets and begins with cardinal and ordinal numbers. It then proceeds through the natural numbers, denumerable sets, rational numbers, and real numbers. The rational numbers are developed in three steps: (1) non-negative fractions, (2) non-negative rational numbers, and (3) the full set of rational numbers. The distinction between these three divisions of the rational numbers is explained fully. Chapter X concludes the study with a discussion of the “axiom of choice” an entity closely related to this study.

Keywords

Discrete mathematics, Numbers-Real, Cardinal numbers, Numbers-Ordinal, Algebra, Classifications

Advisor

Dr. Wilmont Toalson

Date of Award

Summer 1964

Document Type

Thesis - campus only access

DOI

10.58809/IUFF1542

Recommended Citation

Beougher, Elton E., "An Axiomatic Development of the Properties of Real Numbers Through the Use of Set Theory" (1964). Master's Theses. 834.
DOI: 10.58809/IUFF1542
Available at: https://scholars.fhsu.edu/theses/834

Rights

© The Author(s)

Comments

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