Set Theory and Infinity
Set Theory was first developed by Cantor and Dedekind to handle infinite collections. This chapter looks at their theory of countably and uncountably infinite sets. Around 1900, mathematicians were motivated by encountering some perplexing results for infinite sets to provide Set Theory with a more solid foundation. We’ll briefly explore the standard axiomatization of Set Theory, along with its relevance to Peano Arithmetic, and we’ll also look at an application of Set Theory to the theory of computation.