- The principle of set theory known as the Axiom of Choice has been hailed as “probably the most interesting and, in spite of its late appearance, the most discussed axiom of mathematics, second only to Euclid’s axiom of parallels which was introduced more than two thousand years ago” (Fraenkel, Bar-Hillel & Levy 1973, §II.4). The fulsomeness of this description might lead those unfamiliar with the axiom to expect it to be as startling as, say, the Principle of the Constancy of the Velocity of Light or the Heisenberg Uncertainty Principle. But in fact the Axiom of Choice as it is usually stated appears humdrum, even self-evident. For it amounts to nothing more than the claim that, given any collection of mutually disjoint nonempty sets, it is possible to assemble a new set—a transversal or choice set—containing exactly one element from each member of the given collection. Nevertheless, this seemingly innocuous principle has far-reaching mathematical consequences—many indispensable, some startling—and has come to figure prominently in discussions on the foundations of mathematics. It (or its equivalents) have been employed in countless mathematical papers, and a number of monographs have been exclusively devoted to it.
- The Wonderful Wizard of Oz (Wikipedia)
The Wonderful Wizard of Oz is a 1900 children’s novel written by author L. Frank Baum and illustrated by W. W. Denslow. It is the first novel in the Oz series of books. A Kansas farm girl named Dorothy ends up in the magical Land of Oz after she and her pet dog Toto are swept away from their home by a cyclone. Upon her arrival in the magical world of Oz, she learns she cannot return home until she has destroyed the Wicked Witch of the West.
stanford encyclopedia of philosophy of