Year of Award
Bachelor of Arts (BA)
College of Arts & Sciences
Math and Computer Science
Mary Teresine Lewis
Georg Cantor, finite, cardinal, rational, transfinite, infinity
Ever since my high school days, when I worked in trigonometry with infinity, I was curious about its meaning. There was some kind of infinity between the numbers zero (0) and one (1); the counting numbers were infinite; there was a relation between an asymptote of a curve and infinity. Was this all the same concept? Cound one idea relate to the various different usages? These are the questions I asked myself as I began my research into the topic of infinity. I soon discovered that the workings of infinity were much more involved than I thought. There is even an algebra of infinity! In the following pages, I am going to describe my findings. First, I will describe some of the false notions about the concept; and, then I will tell of the man who really laid the groundwork for the development of transfinite numbers. This man is Georg Cantor. In the next section, the basic foundations of the algebra of infinity will be discussed and this will be followed by the enumeration of a few practical applications. The treatment of transfinite numbers would not be complete without a discussion of the paradoxes of infinity and their resolutions if they have been discovered. This is the last part of the paper. We shall now see the real necessity for the development of the concept of infinity by investigating some of the common false notions about the subject.
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Frintrup, Peggy, "Foundations of Transfinite Numbers" (1967). All Theses, Dissertations, and Capstone Projects. 68.
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