ABSTRACT
In the preceding chapter, we left unanswered a fundamental question: Which sets can be well-ordered? Interestingly, the question was posed in this form only at a later stage in the development of set theory. Cantor considered it quite obvious that every set can be well-ordered. Here is a fairly intuitive "proof" of this "fact." In order to well-order a set A, it suffices to construct a one-to-one mapping of some ordinal λ onto A. We proceed by transfinite recursion. Let a be any set not in A. Define
