The Use of the Dedekind Cut in a Postulational Approach to Demonstrate that the Real Number System is a Complete Archimedean Ordered Field

Author

Jean Ann Makowski Peterson, Marquette University

Date of Award

6-1972

Document Type

Master's Essay - Restricted

Degree Name

Master of Science (MS)

Department

Mathematical and Statistical Sciences

First Advisor

Chris C. Braunschweiger

Abstract

Mathematicians have divided the great bulk of existing mathematics into three large categories - geometry, algebra, and analysis, However, this type of classification is largely based on historical and traditional grounds, and as a result, the boundaries between these categories are becoming less and less well defined, There are topics of mathematics in which there is little agreement regarding the category into which they should be placed. For example, topology in its early stages was regarded as geometric, but now it has been so developed that it may constitute an independent fourth division of mathematics. Nevertheless, in spite of such borderline cases, this classification is reasonably sound; for most branches of mathematics have starting points in Euclidean geometry, symbolized arithmetic, or the limit processes of the calculus.

Comments

A Master's Essay Presented to the Faculty of the Mathematics Department of Marquette University, Milwaukee, Wisconsin, In Partial Fulfillment Of the Requirements for the Degree Master of Mathematics

Recommended Citation

Peterson, Jean Ann Makowski, "The Use of the Dedekind Cut in a Postulational Approach to Demonstrate that the Real Number System is a Complete Archimedean Ordered Field" (1972). Master's Theses (1922-2009) Access restricted to Marquette Campus. 5774.
https://epublications.marquette.edu/theses/5774