ABSTRACT
Borel canvassed opinions of the most prominent French mathematicians of his generation — Hadamard, Baire, and Lebesgue — with the upshot that Hadamard sided with Zermelo whereas Baire and Lebesgue seconded Borel. At first blush Borel’s strident reaction against the axiom of choice utilized in Cantor’s new theory of sets is surprising as the French analysts had used and continued to use choice principles routinely in their work. However, in the context of 19th century classical analysis only the Axiom of Dependent
Choices, D C , is invoked and considered to be natural, while the full axiom of choice is unnecessary and even has some counterintuitive consequences.
