Math Squad

To Infinity and Beyond. Introduction
Review of Set Theory
Functions
Countability
Cardinality
Hilbert's Grand Hotel




To Infinity and Beyond

A Review of Set Theory

by Maliha Hossain, proud member of the Math Squad



Georg Cantor called a set a collection of objects. This simple idea was so profound that it has become the foundation of every branch of mathematics. Cantor's theories became an important tool that allowed mathematicians to precisely define concepts such as real numbers, points in space, and continuous functions. In addition, Cantor's theory of sets provided startling new insight into the nature of infinity among which was the fact that some infinite magnitudes are larger than others. We will explore this idea more deeply in this section of the tutorial by studying the following topics



References

  • J. Lewin, "Elements of Set Theory" in An Interactive Introduction to Mathematical Analysis, Cambridge, UK: Cambridge University Press. 2003 ch. 4, pp 50-51



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