Date of Award
Master of Science
Many of the ideas of mathematics have come about because of certain properties of the real numbers. Some of these are convergence, metric spaces, abstract measure theory, and topology.
Because of the beauty and interest of the real number system, it is the most used "concrete" example to express the abstract ideas in a mathematical system. Set theory is another important tool in modern mathematics. Most of our important concepts in modern mathematics are based on set theory. In this paper, we examine some properties shared by both the real numbers and subsets of a given set.
The theorems presented will relate to three areas of mathematics namely, analysis and limiting processes, algebra and partially ordered spaces and topology. The paper begins with definitions and notations. Chapter II includes pre^ liminary theorems and lemmas. Chapter III contains a series of theorems shared by the real numbers and subsets of a given set. We conclude with chapter IV, which relates some algebraic and topological properties of subsets of X.
Prairie View Agriculture And Mechanical College
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Date of Digitization
John B Coleman Library
City of Publication
Armstrong, D. F. (1970). Brief Treatise On Some Comparable Properties Of Sets And Number. Retrieved from https://digitalcommons.pvamu.edu/pvamu-theses/1448