ABSTRACT
The theory of cardinality gives a rigorous way to measure and compare the size of various sets (finite or infinite). This chapter provides the definition and Properties of finite sets and infinite sets. It examines countably infinite sets, which are the smallest infinite sets, and compares the size (cardinality) of two arbitrary sets. The chapter presents the study of countable sets, which are sets that are either finite or countably infinite. The main results of the study are: any subset of a countable set is countable; products of finitely many countable sets are countable; and unions of countably many countable sets are countable. One of the unintuitive aspects of cardinality theory is that there are many different “sizes” of infinite sets. The chapter provides the proof of the Cantor’s theorem and the Schröder–Bernstein theorem.
