eastbound on Interstate 90
- 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.
- South Dakota (Wikipedia)
South Dakota (/- dəˈkoʊtə/; Sioux: Dakȟóta itókaga, pronounced [daˈkˣota iˈtokaga]) is a U.S. state in the North Central region of the United States. It is also part of the Great Plains. South Dakota is named after the Dakota Sioux Native American tribe, which comprises a large portion of the population with nine reservations currently in the state and have historically dominated the territory. South Dakota is the seventeenth largest by area, but the 5th least populous, and the 5th least densely populated of the 50 United States. As the southern part of the former Dakota Territory, South Dakota became a state on November 2, 1889, simultaneously with North Dakota. They are the 39th and 40th states admitted to the union; President Benjamin Harrison shuffled the statehood papers before signing them so that no one could tell which became a state first. Pierre is the state capital, and Sioux Falls, with a population of about 192,200, is South Dakota’s largest city.
