number Basic element of mathematics used for counting, measuring, solving equations, and comparing quantities. They fall into several cat¬ egories. The counting numbers are the familiar 1, 2, 3 ... ; whole num¬ bers are the counting numbers and zero; integers are the whole numbers and the negative counting numbers; and the rational numbers are all pos¬ sible quotients formed by integers, including fractions. These numbers can be symbolically represented by terminating or repeating decimals. Irrational numbers cannot be represented by fractions of integers or repeat¬ ing decimals and must be represented by special symbols such as V2, e, and k. Together, the rational and irrational numbers constitute the real numbers, which form an algebraic field (see field theory), as do the complex numbers. While the counting numbers and rational numbers come about as the means of counting, calculating, and measuring, the others arose as means of solving equations. See also transcendental number.
number system Method of writing numerals to represent numbers. The use of zero as a placeholder was the greatest advance in number sys¬ tems. The most common system is the decimal system, in which 10 sym¬ bols (the Hindu-Arabic numerals) denote multiples of powers of 10 by their position relative to the decimal point. Computers have brought greater awareness of the binary number system, in which two symbols, 0 and 1, represent multiples of powers of 2.
number theory Branch of mathematics concerned with properties of and relations among integers. It is a popular subject among amateur math¬ ematicians and students because of the wealth of seemingly simple prob¬ lems that can be posed. Answers are much harder to come up with. It has been said that any unsolved mathematical problem of any interest more than a century old belongs to number theory. One of the best examples, recently solved, is Fermat's last theorem.
numerical analysis Branch of applied mathematics that studies meth¬ ods for solving complicated equations using arithmetic operations, often so complex that they require a computer, to approximate the processes of analysis (i.e., calculus). The arithmetic model for such an approximation is called an algorithm, the set of procedures the computer executes is called a program, and the commands that carry out the procedures are called code. An example is an algorithm for deriving n by calculating the perimeter of a regular polygon as its number of sides becomes very large. Numeri¬ cal analysis is concerned not just with the numerical result of such a pro¬ cess but with determining whether the error at any stage is within acceptable bounds.
numerical control (NC) Control of a system or device by direct input of data in the form of numbers, letters, symbols, words, or a combination of these forms. It is a principal element of computer-integrated manufac¬ turing, particularly for controlling the operation of machine tools. NC is also essential to the operation of modern industrial robots. The two basic types of NC systems are point-to-point, in which a device is programmed to perform a series of motions with fixed starting and stopping points, and continuous-path, in which a point-to-point programmed device has suf¬ ficient memory to be “aware” of its former actions and their results and to act in accordance with this information.
numerology Use of numbers to interpret a person’s character or divine the future. It is based on the assertion by Pythagoras that all things can be expressed in numerical terms because they are ultimately reducible to num¬ bers. Using a method analogous to that of the Greek and Hebrew alphabets (in which each letter also represented a number), modern numerology attaches a series of digits to an inquirer’s name and uses these, along with the date of birth, to reveal the person’s true nature and prospects.
Numidia \nu-'mi-de-9\ Ancient country, North Africa, approximately coextensive with modern Algeria. During the Second Punic War (see Punic
wars), its two great tribes divided, one supporting the Romans and the other the Carthaginians. The tribal chief Masinissa was made king of Numidia after the Roman victory in 201 bc. After the destruction of Carthage, thousands fled to Numidia, which became a Roman province in 46 bc. Its capital was Cirta, and the chief city was Hippo, which was the see of St. Augustine. After its conquest by the Vandals in ad 429, Roman civilization there declined rapidly; some pockets of native culture survived, however, and even continued after the Arab conquest in the 8th century.
Nun \'niin\ or Nu Oldest of the Egyptian gods and father of Re, the sun god. Nun represented the dark, turbulent waters out of which the cosmos was churned. Since it was believed that the primeval ocean continued to surround the ordered cosmos, the creation myth was reenacted each day as the sun rose from the waters. Nun was also thought to exist as subsoil water and as the source of the annual flooding of the Nile.
Nun River \'nim\ River, southern Nigeria. Considered the direct con¬ tinuation of the Niger River, it flows southwest to the Gulf of Guinea, at Akassa. It was a trade route in the 19th century, when the Igbo kingdom controlled commerce. Petroleum was discovered along the Nun in 1963, and oil is piped from the oil fields along the Trans-Niger Pipeline.
Nunavut Vnii-no-.vihA Territory (pop., 2001: 26,745), north-central Canada. Nunavut (Inuit: “Our Land”) is the result of Canada’s largest land claim settlement, created to give the Inuit (see Eskimo), representing 85% of its population, a greater voice in Canadian government. Occupying an area of 772,000 sq mi (2,000,000 sq km), or one-fifth of Canada’s land- mass, it comprises the central and eastern parts of the former Northwest Territories, including Baffin and Ellesmere islands. Its capital is Iqaluit. The area was settled by Inuit from 4500 bc to ad 1000. Vikings probably vis¬ ited during the Middle Ages, but the first records of exploration are from Martin Frobisher’s 1576 search for the Northwest Passage. The mainland was explored by Englishman Samuel Heame in 1770-72. After passing through British possession, it was transferred to Canada in 1870. In 1976 a political organization called for the creation of a territory to settle Inuit claims in the Northwest Territories. The proposal was approved by the Canadian government in 1993. Nunavut’s first elections were held in February 1999, and the territory was inaugurated on April 1, 1999.
Nur al-HilmT Vnur-al-'hil-meV, Burhanuddin bin Muhammad
(b. 1911, Kota Bharu, Malaya—d. Oct. 25, 1969, Taiping, Malaysia) Malay nationalist leader. After serving the administration of the Japanese occupation during the war, Nur al-Hilml became a prominent left-wing leader who worked for an independent and multiracial Malaysia. In 1956 he became president of the Pan-Malayan Islamic Party, which became the principal opposition party in Malaysian politics. Detained in 1965 for allegedly pro-Indonesian activities, he was released in 1966; he remained nominal president of the party until his death.
Nuremberg See Nurnberg
Nureyev \nu-'ra-yef\, Rudolf (Hametovich) (b. March 17, 1938, Irkutsk, Russia, U.S.S.R.—d. Jan. 6,
1993, Paris, Fr.) Russian ballet dancer. After studying ballet in Len¬ ingrad (1955—58), he joined the Kirov Ballet as a soloist. He defected during the company’s tour to Paris in 1961. Thereafter he danced as a guest artist with many companies, especially the Royal Ballet, where he regularly partnered Margot Fonteyn.
His performances, combining an intensely romantic sensibility with stunning muscularity and technique, made him an international star. He choreographed new versions of Romeo and Juliet, Manfred, and The Nutcracker. From 1983 to 1989 he was artistic director of the Paris Opera Ballet.