"One inexperienced in higher mathematics may very well question the necessity of irrational numbers since all numbers used in computation are rational. For example, one computes the area of a circle by using the formula A = [pi]r² and substituting 22/7 or some other approximate value for [pi]. Furthermore, the rational numbers are dense on the straight line, and so physical means can be used to determine whether a given length or ratio is rational. However, in theoretical mathematics there is a need for a real number system to give all limiting values. Calculus, as we know it, could not exist without the irrational numbers. The purpose of this paper is to make a careful study of the real number system, to develop some criteria for the irrationality of certain numbers, and to analyze the proofs of the irrationality of a few simple irrational numbers"--Preface. / "January 1959." / Typescript. / "Submitted to the Graduate Council of Florida State University in partial fulfillment of the requirements for the degree of Master of Science." / Advisor: Paul J. McCarthy, Professor Directing Paper. / Includes bibliographical references (leaf 36).
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_257120 |
| Contributors | Edwards, Valma Y. (authoraut), McCarthy, Paul J. (professor directing thesis.), Florida State University (degree granting institution) |
| Publisher | Florida State University, Florida State University |
| Source Sets | Florida State University |
| Language | English, English |
| Detected Language | English |
| Type | Text, text |
| Format | 1 online resource (iii, 36 leaves), computer, application/pdf |
| Rights | This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s). The copyright in theses and dissertations completed at Florida State University is held by the students who author them. |
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