- Altair is the brightest star in the constellation of Aquila and the twelfth-brightest star in the night sky. It has the Bayer designation Alpha Aquilae, which is Latinised from α Aquilae and abbreviated Alpha Aql or α Aql. Altair is an A-type main-sequence star with an apparent visual magnitude of 0.77 and is one of the vertices of the Summer Triangle asterism; the other two vertices are marked by Deneb and Vega. It is located at a distance of 16.7 light-years (5.1 parsecs) from the Sun. Altair is currently in the G-cloud—a nearby interstellar cloud, an accumulation of gas and dust.
- 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.