 The Axiom of Choice states: For every set \(A\) of non-empty sets, there exists a set that has exactly one element in common with each set in \(A\). This started a whole era during which the Axiom of Choice was treated most carefully as a dubious hypothesis (see the monumental study by Moore 1982). And that is ironic, for, among all of the usual principles of set theory, the Axiom of Choice is the only one that explicitly enforces the existence of some arbitrary subsets. But, important as this idea had been in motivating Cantor and Dedekind, and however entangled it is with classical analysis, infinite arbitrary subsets were rejected by many other authors. Among the most influential ones in the following period, one ought to emphasize the names of Russell, Hermann Weyl, and of course Brouwer.