Curious about Cantor

By Katie Warnken and Charnae Wilson

29 March 2019

This presentation will discuss the Cantor Set and its properties. Georg Cantor studied this set in the nineteenth century, and we still use his ideas about different sizes of infinite today. This unusual set can be used in a variety of areas in Mathematics, including Real Analysis, Geometry, and topology. The properties that we will prove in this presentation are the length of the Cantor Set is zero and the cardinality of the Cantor Set is 2ℵ0. This categorizes the Cantor Set as a large, yet also small, set. While this can be mind-boggling for some, it can also open our eyes to another world of mathematics, as it did for Georg Cantor and other mathematicians in the nineteenth century. We will also discuss applications of continuing fractions to the Cantor set, among other curiosities.