Book:Gerald B. Folland/Real Analysis: Modern Techniques and their Applications/Errata

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Errata for 1984: Gerald B. Folland: Real Analysis: Modern Techniques and their Applications

Zorn's Lemma Implies Zermelo's Well-Ordering Theorem

Prologue: $2$. Orderings: $(\text P.3)$:

Every nonempty set $X$ can be well-ordered.

Consider the collection $\WW$ of well orderings of subsets of $X$.
Such well orderings may be regarded as subsets of $X \times X$, so $\WW$ is partially ordered by inclusion.
It is easy to verify that the hypotheses of Zorn's lemma are satisfied, so $\WW$ has a maximal element.