- The Axiom of Choice (Stanford Encyclopedia of Philosophy)
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.
- James Monroe (Wikipedia)
James Monroe (/mənˈroʊ/ mən-ROH; April 28, 1758 – July 4, 1831) was an American statesman, lawyer, diplomat, and Founding Father who served as the fifth president of the United States from 1817 to 1825. He was the last Founding Father to serve as president as well as the last president of the Virginia dynasty. He was a member of the Democratic-Republican Party, and his presidency coincided with the Era of Good Feelings, concluding the First Party System era of American politics. He issued the Monroe Doctrine, a policy of limiting European colonialism in the Americas. Monroe previously served as governor of Virginia, a member of the United States Senate, U.S. ambassador to France and Britain, the seventh secretary of state, and the eighth secretary of war.