English Numbers [UPD]
Antonette Hespe
The show uses the number three in its title instead of the letter "e", in which is found in Leetspeak. In the interviews with Tom Jicha of the South Florida Sun-Sentinel and with Alan Pergament of The Buffalo News, Heuton mentioned that the use of the number three in the title derives from leet, a form of computer jargon that replaces letters with numbers.[52][53] Dr. Gary Lorden, a California Institute of Technology mathematics professor who served as the show's mathematics consultant, told NPR's Ira Flatow that it was created on a normal computer keyboard. Lorden also mentioned that the use of the number three in the title can serve as a restriction in Internet searches about the series.[54]
Both entertainment reporters and psychologists noticed the title's spelling. Some reporters, such as Joanne Ostrow of the Denver Post,[55] the staff members of People Magazine,[56] the editors of The Futon Critic,[57] the staff of the Scripps Howard News Service,[58] and Mike Hughes of USA Today[59] acknowledged the presence of the number three in the title. Lynette Rice of Entertainment Weekly asked Krumholtz about the three in the title; his response was, "Isn't that annoying? I think it should be the mathematical symbol for sigma, which looks like an E. I've been fighting that for weeks."[60] (The sigma (Σ) stands for summation.[61]) Others used varying adjectives to describe the title. The TV site Zap2it.com called it "their typographical silliness, not ours".[62] Brad Aspey of The Muskegon Chronicle, stated, "No, that wasn't an ugly typo you just read - "NUMB3RS" (pronounced numbers) is the idiosyncratic title of filmmakers Ridley and Tony Scott's astute and crafty psychological drama which shows that even math can make for edge-of-your-seat entertainment."[63] Ellen Gray of The Philadelphia Daily News, said, "Some of you may have noticed that in promoting "Numb3rs," which premieres Sunday before moving to its regular 10 p.m. Friday slot, CBS has chosen to put a 3 in place of the "e" in the title....I won't be going along with this particular affectation, which slows down my typing and seems to be the graphic equivalent of the reversed "R" in Toys R Us. So there."[64]
Besides their practical uses, numbers have cultural significance throughout the world.[7][8] For example, in Western society, the number 13 is often regarded as unlucky, and "a million" may signify "a lot" rather than an exact quantity.[7] Though it is now regarded as pseudoscience, belief in a mystical significance of numbers, known as numerology, permeated ancient and medieval thought.[9] Numerology heavily influenced the development of Greek mathematics, stimulating the investigation of many problems in number theory which are still of interest today.[9]
During the 19th century, mathematicians began to develop many different abstractions which share certain properties of numbers, and may be seen as extending the concept. Among the first were the hypercomplex numbers, which consist of various extensions or modifications of the complex number system. In modern mathematics, number systems are considered important special examples of more general algebraic structures such as rings and fields, and the application of the term "number" is a matter of convention, without fundamental significance.[10]
Bones and other artifacts have been discovered with marks cut into them that many believe are tally marks.[11] These tally marks may have been used for counting elapsed time, such as numbers of days, lunar cycles or keeping records of quantities, such as of animals.
A tallying system has no concept of place value (as in modern decimal notation), which limits its representation of large numbers. Nonetheless, tallying systems are considered the first kind of abstract numeral system.
Brahmagupta's Brāhmasphuṭasiddhānta is the first book that mentions zero as a number, hence Brahmagupta is usually considered the first to formulate the concept of zero. He gave rules of using zero with negative and positive numbers, such as "zero plus a positive number is a positive number, and a negative number plus zero is the negative number". The Brāhmasphuṭasiddhānta is the earliest known text to treat zero as a number in its own right, rather than as simply a placeholder digit in representing another number as was done by the Babylonians or as a symbol for a lack of quantity as was done by Ptolemy and the Romans.
During the 600s, negative numbers were in use in India to represent debts. Diophantus' previous reference was discussed more explicitly by Indian mathematician Brahmagupta, in Brāhmasphuṭasiddhānta in 628, who used negative numbers to produce the general form quadratic formula that remains in use today. However, in the 12th century in India, Bhaskara gives negative roots for quadratic equations but says the negative value "is in this case not to be taken, for it is inadequate; people do not approve of negative roots".
European mathematicians, for the most part, resisted the concept of negative numbers until the 17th century, although Fibonacci allowed negative solutions in financial problems where they could be interpreted as debts (chapter 13 of Liber Abaci, 1202) and later as losses (in Flos). René Descartes called them false roots as they cropped up in algebraic polynomials yet he found a way to swap true roots and false roots as well. At the same time, the Chinese were indicating negative numbers by drawing a diagonal stroke through the right-most non-zero digit of the corresponding positive number's numeral.[18] The first use of negative numbers in a European work was by Nicolas Chuquet during the 15th century. He used them as exponents, but referred to them as "absurd numbers".
It is likely that the concept of fractional numbers dates to prehistoric times. The Ancient Egyptians used their Egyptian fraction notation for rational numbers in mathematical texts such as the Rhind Mathematical Papyrus and the Kahun Papyrus. Classical Greek and Indian mathematicians made studies of the theory of rational numbers, as part of the general study of number theory.[19] The best known of these is Euclid's Elements, dating to roughly 300 BC. Of the Indian texts, the most relevant is the Sthananga Sutra, which also covers number theory as part of a general study of mathematics.
The earliest known use of irrational numbers was in the Indian Sulba Sutras composed between 800 and 500 BC.[20][better source needed] The first existence proofs of irrational numbers is usually attributed to Pythagoras, more specifically to the Pythagorean Hippasus of Metapontum, who produced a (most likely geometrical) proof of the irrationality of the square root of 2. The story goes that Hippasus discovered irrational numbers when trying to represent the square root of 2 as a fraction. However, Pythagoras believed in the absoluteness of numbers, and could not accept the existence of irrational numbers. He could not disprove their existence through logic, but he could not accept irrational numbers, and so, allegedly and frequently reported, he sentenced Hippasus to death by drowning, to impede spreading of this disconcerting news.[21][better source needed]
The 16th century brought final European acceptance of negative integral and fractional numbers. By the 17th century, mathematicians generally used decimal fractions with modern notation. It was not, however, until the 19th century that mathematicians separated irrationals into algebraic and transcendental parts, and once more undertook the scientific study of irrationals. It had remained almost dormant since Euclid. In 1872, the publication of the theories of Karl Weierstrass (by his pupil E. Kossak), Eduard Heine,[22] Georg Cantor,[23] and Richard Dedekind[24] was brought about. In 1869, Charles Méray had taken the same point of departure as Heine, but the theory is generally referred to the year 1872. Weierstrass's method was completely set forth by Salvatore Pincherle (1880), and Dedekind's has received additional prominence through the author's later work (1888) and endorsement by Paul Tannery (1894). Weierstrass, Cantor, and Heine base their theories on infinite series, while Dedekind founds his on the idea of a cut (Schnitt) in the system of real numbers, separating all rational numbers into two groups having certain characteristic properties. The subject has received later contributions at the hands of Weierstrass, Kronecker,[25] and Méray.
Continued fractions, closely related to irrational numbers (and due to Cataldi, 1613), received attention at the hands of Euler,[26] and at the opening of the 19th century were brought into prominence through the writings of Joseph Louis Lagrange. Other noteworthy contributions have been made by Druckenmüller (1837), Kunze (1857), Lemke (1870), and Günther (1872). Ramus[27] first connected the subject with determinants, resulting, with the subsequent contributions of Heine,[28] Möbius, and Günther,[29] in the theory of Kettenbruchdeterminanten.
In the 1960s, Abraham Robinson showed how infinitely large and infinitesimal numbers can be rigorously defined and used to develop the field of nonstandard analysis. The system of hyperreal numbers represents a rigorous method of treating the ideas about infinite and infinitesimal numbers that had been used casually by mathematicians, scientists, and engineers ever since the invention of infinitesimal calculus by Newton and Leibniz.
The earliest fleeting reference to square roots of negative numbers occurred in the work of the mathematician and inventor Heron of Alexandria in the 1st century AD, when he considered the volume of an impossible frustum of a pyramid. They became more prominent when in the 16th century closed formulas for the roots of third and fourth degree polynomials were discovered by Italian mathematicians such as Niccolò Fontana Tartaglia and Gerolamo Cardano. It was soon realized that these formulas, even if one was only interested in real solutions, sometimes required the manipulation of square roots of negative numbers.
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