  Zermelo asserts that “the purely objective character” of this principle “is immediately evident.” In making this assertion Zermelo meant to emphasize the fact that in this form the principle makes no appeal to the possibility of making “choices”. It may also be that Zermelo had the following “combinatorial” justification of the principle in mind. Given a family \(\sH\) of mutually disjoint nonempty sets, call a subset \(S \subseteq \bigcup \sH\) a selector for \(\sH\) if \(S\cap X \ne \varnothing\) for all \(X \in \sH\). Clearly selectors for \(\sH\) exist; \(\bigcup \sH\) itself is an example. Now one can imagine taking a selector \(S\) for \(\sH\) and “thinning out” each intersection \(S \cap X\) for \(X\in \sH\) until it contains just a single element. The result is a transversal for \(\sH\). This argument, suitably refined, yields a precise derivation of AC in this formulation from the set-theoretical principle known as Zorn’s lemma (see below). 