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An Introduction to Elementary Set Theory

An Introduction to Elementary Set TheoryGuram Bezhanishvili and Eachan Landreth 1 IntroductionIn this project we will learn Elementary set Theory from the original historical sources by two keyfigures in the development of set Theory , Georg Cantor (1845 1918) and Richard Dedekind (1831 1916). We will learn the basic properties of sets, how to define the size of a set, and how to comparedifferent sizes of sets. This will enable us to give precise definitions of finite and infinite sets. Wewill conclude the project by exploring a rather unusual world of infinite Cantor, the founder of set Theory , considered by many as one of the most original mindsin the history of mathematics, was born in St.

teach the theory of real numbers based on Dedekind’s cuts. Dedekind was the rst to introduce the concept of an ideal|a key concept in modern algebra|generalizing the ideal numbers of Ernst Kummer (1810{1893). His contributions to set theory as well as to the study of natural numbers and modular lattices are equally important.

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