Splash Biography

An introduction to infinities, mostly related to the work of Georg Cantor. We'll cover the notion of cardinality of a set and the counter-intuitive ways that cardinality behaves when you have infinite sets. We'll also look at related topics, such as: - Hilbert's paradox of the Grand Hotel - the Continuum Hypothesis - history and philosophy surrounding Cantor's work, if time permits Students should have basic knowledge of sets and maps between sets (injections, surjections, and bijections), and also of proof by contradiction. We'll use common examples of sets, including finite sets, the integers, the real numbers, and power sets. I'll briefly review any of these topics if there are any questions, though!

In this class we'll look at different types of real numbers: rational vs. irrational and algebraic vs. transcendental. There will be some fun problems and proofs to think about - it won't be all definitions!