Cardinalities and Diagonalization

Chapter Summary

This chapter introduced the concept of cardinality and illustrated how various infinite sets might have incomparable cardinalities. The main technique for demonstrating that two sets have different cardinalities is a proof technique by contradiction known as diagonalization. A useful theorem for showing that two sets have the same cardinality is the Schröder-Bernstein theorem. A thorough description of these concepts in this early of a chapter has been found to be helpful to many students when they study later chapters of this book.