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Generalizations and Properties of the Ternary Cantor Set and Explorations in Similar Sets

Stettin, Rebecca A
http://rave.ohiolink.edu/etdc/view?acc_num=auhonors1494171314877262

Abstract Details

2017, Bachelor of Science, Ashland University, Mathematics/Computer Science.
Georg Cantor was made famous by introducing the Cantor set in his works of mathematics. This project focuses on different Cantor sets and their properties. The ternary Cantor set is the most well known of the Cantor sets, and can be best described by its construction. This set starts with the closed interval zero to one, and is constructed in iterations. The first iteration requires removing the middle third of this interval. The second iteration will remove the middle third of each of these two remaining intervals. These iterations continue in this fashion infinitely. Finally, the ternary Cantor set is described as the intersection of all of these intervals. This set is particularly interesting due to its unique properties being uncountable, closed, length of zero, and more. A more general Cantor set is created by taking the intersection of iterations that remove any middle portion during each iteration. This project explores the ternary Cantor set, as well as variations in Cantor sets such as looking at different middle portions removed to create the sets. The project focuses on attempting to generalize the properties of these Cantor sets.
Darren Wick, Ph.D. (Advisor)
Gordon Swain, Ph.D. (Committee Member)
44 p.
Mathematics
Cantor Set; mathematics

Recommended Citations

Citations

  • Stettin, R. A. (2017). Generalizations and Properties of the Ternary Cantor Set and Explorations in Similar Sets [Undergraduate thesis, Ashland University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=auhonors1494171314877262

    APA Style (7th edition)

  • Stettin, Rebecca. Generalizations and Properties of the Ternary Cantor Set and Explorations in Similar Sets. 2017. Ashland University, Undergraduate thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=auhonors1494171314877262.

    MLA Style (8th edition)

  • Stettin, Rebecca. "Generalizations and Properties of the Ternary Cantor Set and Explorations in Similar Sets." Undergraduate thesis, Ashland University, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=auhonors1494171314877262

    Chicago Manual of Style (17th edition)

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This open access ETD is published by Ashland University Honors Theses and OhioLINK.