1.
I Feel It/Thousand
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I Feel It and Thousand are two songs by the American electronica musician Moby, released as a double A-side single from his first album, Moby. Thousand has the Guinness world record for the fastest tempo in beats-per-minute of any released single and it clocks in at approximately 1,000 BPM, hence the title of the recording. The single peaked at number 38 on the UK Singles Chart
2.
Integer
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An integer is a number that can be written without a fractional component. For example,21,4,0, and −2048 are integers, while 9.75, 5 1⁄2, the set of integers consists of zero, the positive natural numbers, also called whole numbers or counting numbers, and their additive inverses. This is often denoted by a boldface Z or blackboard bold Z standing for the German word Zahlen, ℤ is a subset of the sets of rational and real numbers and, like the natural numbers, is countably infinite. The integers form the smallest group and the smallest ring containing the natural numbers, in algebraic number theory, the integers are sometimes called rational integers to distinguish them from the more general algebraic integers. In fact, the integers are the integers that are also rational numbers. Like the natural numbers, Z is closed under the operations of addition and multiplication, that is, however, with the inclusion of the negative natural numbers, and, importantly,0, Z is also closed under subtraction. The integers form a ring which is the most basic one, in the following sense, for any unital ring. This universal property, namely to be an object in the category of rings. Z is not closed under division, since the quotient of two integers, need not be an integer, although the natural numbers are closed under exponentiation, the integers are not. The following lists some of the properties of addition and multiplication for any integers a, b and c. In the language of algebra, the first five properties listed above for addition say that Z under addition is an abelian group. As a group under addition, Z is a cyclic group, in fact, Z under addition is the only infinite cyclic group, in the sense that any infinite cyclic group is isomorphic to Z. The first four properties listed above for multiplication say that Z under multiplication is a commutative monoid. However, not every integer has an inverse, e. g. there is no integer x such that 2x =1, because the left hand side is even. This means that Z under multiplication is not a group, all the rules from the above property table, except for the last, taken together say that Z together with addition and multiplication is a commutative ring with unity. It is the prototype of all objects of algebraic structure. Only those equalities of expressions are true in Z for all values of variables, note that certain non-zero integers map to zero in certain rings. The lack of zero-divisors in the means that the commutative ring Z is an integral domain
3.
Negative number
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In mathematics, a negative number is a real number that is less than zero. If positive represents movement to the right, negative represents movement to the left, if positive represents above sea level, then negative represents below level. If positive represents a deposit, negative represents a withdrawal and they are often used to represent the magnitude of a loss or deficiency. A debt that is owed may be thought of as a negative asset, if a quantity may have either of two opposite senses, then one may choose to distinguish between those senses—perhaps arbitrarily—as positive and negative. In the medical context of fighting a tumor, an expansion could be thought of as a negative shrinkage, negative numbers are used to describe values on a scale that goes below zero, such as the Celsius and Fahrenheit scales for temperature. The laws of arithmetic for negative numbers ensure that the common idea of an opposite is reflected in arithmetic. For example, − −3 =3 because the opposite of an opposite is the original thing, negative numbers are usually written with a minus sign in front. For example, −3 represents a quantity with a magnitude of three, and is pronounced minus three or negative three. To help tell the difference between a subtraction operation and a number, occasionally the negative sign is placed slightly higher than the minus sign. Conversely, a number that is greater than zero is called positive, the positivity of a number may be emphasized by placing a plus sign before it, e. g. +3. In general, the negativity or positivity of a number is referred to as its sign, every real number other than zero is either positive or negative. The positive whole numbers are referred to as natural numbers, while the positive and negative numbers are referred to as integers. In bookkeeping, amounts owed are often represented by red numbers, or a number in parentheses, Liu Hui established rules for adding and subtracting negative numbers. By the 7th century, Indian mathematicians such as Brahmagupta were describing the use of negative numbers, islamic mathematicians further developed the rules of subtracting and multiplying negative numbers and solved problems with negative coefficients. Western mathematicians accepted the idea of numbers by the 17th century. Prior to the concept of numbers, mathematicians such as Diophantus considered negative solutions to problems false. Negative numbers can be thought of as resulting from the subtraction of a number from a smaller. For example, negative three is the result of subtracting three from zero,0 −3 = −3, in general, the subtraction of a larger number from a smaller yields a negative result, with the magnitude of the result being the difference between the two numbers
4.
Factorization
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In mathematics, factorization or factoring is the decomposition of an object into a product of other objects, or factors, which when multiplied together give the original. For example, the number 15 factors into primes as 3 ×5, in all cases, a product of simpler objects is obtained. The aim of factoring is usually to reduce something to “basic building blocks”, such as numbers to prime numbers, factoring integers is covered by the fundamental theorem of arithmetic and factoring polynomials by the fundamental theorem of algebra. Viètes formulas relate the coefficients of a polynomial to its roots, the opposite of polynomial factorization is expansion, the multiplying together of polynomial factors to an “expanded” polynomial, written as just a sum of terms. Integer factorization for large integers appears to be a difficult problem, there is no known method to carry it out quickly. Its complexity is the basis of the security of some public key cryptography algorithms. A matrix can also be factorized into a product of matrices of special types, One major example of this uses an orthogonal or unitary matrix, and a triangular matrix. There are different types, QR decomposition, LQ, QL, RQ and this situation is generalized by factorization systems. By the fundamental theorem of arithmetic, every integer greater than 1 has a unique prime factorization. Given an algorithm for integer factorization, one can factor any integer down to its constituent primes by repeated application of this algorithm, for very large numbers, no efficient classical algorithm is known. Modern techniques for factoring polynomials are fast and efficient, but use sophisticated mathematical ideas and these techniques are used in the construction of computer routines for carrying out polynomial factorization in Computer algebra systems. This article is concerned with classical techniques. While the general notion of factoring just means writing an expression as a product of simpler expressions, when factoring polynomials this means that the factors are to be polynomials of smaller degree. Thus, while x 2 − y = is a factorization of the expression, another issue concerns the coefficients of the factors. It is not always possible to do this, and a polynomial that can not be factored in this way is said to be irreducible over this type of coefficient, thus, x2 -2 is irreducible over the integers and x2 +4 is irreducible over the reals. In the first example, the integers 1 and -2 can also be thought of as real numbers, and if they are, then x 2 −2 = shows that this polynomial factors over the reals. Similarly, since the integers 1 and 4 can be thought of as real and hence complex numbers, x2 +4 splits over the complex numbers, i. e. x 2 +4 =. The fundamental theorem of algebra can be stated as, Every polynomial of n with complex number coefficients splits completely into n linear factors
5.
Divisor
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In mathematics, a divisor of an integer n, also called a factor of n, is an integer m that may be multiplied by some other integer to produce n. In this case one says also that n is a multiple of m, an integer n is divisible by another integer m if m is a divisor of n, this implies dividing n by m leaves no remainder. Under this definition, the statement m ∣0 holds for every m, as before, but with the additional constraint k ≠0. Under this definition, the statement m ∣0 does not hold for m ≠0, in the remainder of this article, which definition is applied is indicated where this is significant. Divisors can be negative as well as positive, although sometimes the term is restricted to positive divisors. For example, there are six divisors of 4, they are 1,2,4, −1, −2, and −4,1 and −1 divide every integer. Every integer is a divisor of itself, every integer is a divisor of 0. Integers divisible by 2 are called even, and numbers not divisible by 2 are called odd,1, −1, n and −n are known as the trivial divisors of n. A divisor of n that is not a divisor is known as a non-trivial divisor. A non-zero integer with at least one divisor is known as a composite number, while the units −1 and 1. There are divisibility rules which allow one to recognize certain divisors of a number from the numbers digits, the generalization can be said to be the concept of divisibility in any integral domain. 7 is a divisor of 42 because 7 ×6 =42 and it can also be said that 42 is divisible by 7,42 is a multiple of 7,7 divides 42, or 7 is a factor of 42. The non-trivial divisors of 6 are 2, −2,3, the positive divisors of 42 are 1,2,3,6,7,14,21,42. 5 ∣0, because 5 ×0 =0, if a ∣ b and b ∣ a, then a = b or a = − b. If a ∣ b and a ∣ c, then a ∣ holds, however, if a ∣ b and c ∣ b, then ∣ b does not always hold. If a ∣ b c, and gcd =1, then a ∣ c, if p is a prime number and p ∣ a b then p ∣ a or p ∣ b. A positive divisor of n which is different from n is called a proper divisor or a part of n. A number that does not evenly divide n but leaves a remainder is called an aliquant part of n, an integer n >1 whose only proper divisor is 1 is called a prime number
6.
Greek numerals
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Greek numerals are a system of writing numbers using the letters of the Greek alphabet. These alphabetic numerals are known as Ionic or Ionian numerals, Milesian numerals. In modern Greece, they are used for ordinal numbers. For ordinary cardinal numbers, however, Greece uses Arabic numerals, attic numerals, which were later adopted as the basis for Roman numerals, were the first alphabetic set. They were acrophonic, derived from the first letters of the names of the numbers represented and they ran =1, =5, =10, =100, =1000, and =10000. 50,500,5000, and 50000 were represented by the letter with minuscule powers of ten written in the top right corner, the same system was used outside of Attica, but the symbols varied with the local alphabets, in Boeotia, was 1000. The present system probably developed around Miletus in Ionia, 19th-century classicists placed its development in the 3rd century BC, the occasion of its first widespread use. The present system uses the 24 letters adopted by Euclid as well as three Phoenician and Ionic ones that were not carried over, digamma, koppa, and sampi. The position of characters within the numbering system imply that the first two were still in use while the third was not. Greek numerals are decimal, based on powers of 10, the units from 1 to 9 are assigned to the first nine letters of the old Ionic alphabet from alpha to theta. Each multiple of one hundred from 100 to 900 was then assigned its own separate letter as well and this alphabetic system operates on the additive principle in which the numeric values of the letters are added together to obtain the total. For example,241 was represented as, in ancient and medieval manuscripts, these numerals were eventually distinguished from letters using overbars, α, β, γ, etc. In medieval manuscripts of the Book of Revelation, the number of the Beast 666 is written as χξϛ, although the Greek alphabet began with only majuscule forms, surviving papyrus manuscripts from Egypt show that uncial and cursive minuscule forms began early. These new letter forms sometimes replaced the ones, especially in the case of the obscure numerals. The old Q-shaped koppa began to be broken up and simplified, the numeral for 6 changed several times. During antiquity, the letter form of digamma came to be avoided in favor of a special numerical one. By the Byzantine era, the letter was known as episemon and this eventually merged with the sigma-tau ligature stigma. In modern Greek, a number of changes have been made
7.
Roman numerals
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The numeric system represented by Roman numerals originated in ancient Rome and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages. Numbers in this system are represented by combinations of letters from the Latin alphabet, Roman numerals, as used today, are based on seven symbols, The use of Roman numerals continued long after the decline of the Roman Empire. The numbers 1 to 10 are usually expressed in Roman numerals as follows, I, II, III, IV, V, VI, VII, VIII, IX, Numbers are formed by combining symbols and adding the values, so II is two and XIII is thirteen. Symbols are placed left to right in order of value. Named after the year of its release,2014 as MMXIV, the year of the games of the XXII Olympic Winter Games The standard forms described above reflect typical modern usage rather than a universally accepted convention. Usage in ancient Rome varied greatly and remained inconsistent in medieval, Roman inscriptions, especially in official contexts, seem to show a preference for additive forms such as IIII and VIIII instead of subtractive forms such as IV and IX. Both methods appear in documents from the Roman era, even within the same document, double subtractives also occur, such as XIIX or even IIXX instead of XVIII. Sometimes V and L are not used, with such as IIIIII. Such variation and inconsistency continued through the period and into modern times. Clock faces that use Roman numerals normally show IIII for four o’clock but IX for nine o’clock, however, this is far from universal, for example, the clock on the Palace of Westminster in London uses IV. Similarly, at the beginning of the 20th century, different representations of 900 appeared in several inscribed dates. For instance,1910 is shown on Admiralty Arch, London, as MDCCCCX rather than MCMX, although Roman numerals came to be written with letters of the Roman alphabet, they were originally independent symbols. The Etruscans, for example, used
8.
Greek language
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Greek is an independent branch of the Indo-European family of languages, native to Greece and other parts of the Eastern Mediterranean. It has the longest documented history of any living language, spanning 34 centuries of written records and its writing system has been the Greek alphabet for the major part of its history, other systems, such as Linear B and the Cypriot syllabary, were used previously. The alphabet arose from the Phoenician script and was in turn the basis of the Latin, Cyrillic, Armenian, Coptic, Gothic and many other writing systems. Together with the Latin texts and traditions of the Roman world, during antiquity, Greek was a widely spoken lingua franca in the Mediterranean world and many places beyond. It would eventually become the official parlance of the Byzantine Empire, the language is spoken by at least 13.2 million people today in Greece, Cyprus, Italy, Albania, Turkey, and the Greek diaspora. Greek roots are used to coin new words for other languages, Greek. Greek has been spoken in the Balkan peninsula since around the 3rd millennium BC, the earliest written evidence is a Linear B clay tablet found in Messenia that dates to between 1450 and 1350 BC, making Greek the worlds oldest recorded living language. Among the Indo-European languages, its date of earliest written attestation is matched only by the now extinct Anatolian languages, the Greek language is conventionally divided into the following periods, Proto-Greek, the unrecorded but assumed last ancestor of all known varieties of Greek. The unity of Proto-Greek would have ended as Hellenic migrants entered the Greek peninsula sometime in the Neolithic era or the Bronze Age, Mycenaean Greek, the language of the Mycenaean civilisation. It is recorded in the Linear B script on tablets dating from the 15th century BC onwards, Ancient Greek, in its various dialects, the language of the Archaic and Classical periods of the ancient Greek civilisation. It was widely known throughout the Roman Empire, after the Roman conquest of Greece, an unofficial bilingualism of Greek and Latin was established in the city of Rome and Koine Greek became a first or second language in the Roman Empire. The origin of Christianity can also be traced through Koine Greek, Medieval Greek, also known as Byzantine Greek, the continuation of Koine Greek in Byzantine Greece, up to the demise of the Byzantine Empire in the 15th century. Much of the written Greek that was used as the language of the Byzantine Empire was an eclectic middle-ground variety based on the tradition of written Koine. Modern Greek, Stemming from Medieval Greek, Modern Greek usages can be traced in the Byzantine period and it is the language used by the modern Greeks, and, apart from Standard Modern Greek, there are several dialects of it. In the modern era, the Greek language entered a state of diglossia, the historical unity and continuing identity between the various stages of the Greek language is often emphasised. Greek speakers today still tend to regard literary works of ancient Greek as part of their own rather than a foreign language and it is also often stated that the historical changes have been relatively slight compared with some other languages. According to one estimation, Homeric Greek is probably closer to demotic than 12-century Middle English is to modern spoken English, Greek is spoken by about 13 million people, mainly in Greece, Albania and Cyprus, but also worldwide by the large Greek diaspora. Greek is the language of Greece, where it is spoken by almost the entire population
9.
Latin
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Latin is a classical language belonging to the Italic branch of the Indo-European languages. The Latin alphabet is derived from the Etruscan and Greek alphabets, Latin was originally spoken in Latium, in the Italian Peninsula. Through the power of the Roman Republic, it became the dominant language, Vulgar Latin developed into the Romance languages, such as Italian, Portuguese, Spanish, French, and Romanian. Latin, Italian and French have contributed many words to the English language, Latin and Ancient Greek roots are used in theology, biology, and medicine. By the late Roman Republic, Old Latin had been standardised into Classical Latin, Vulgar Latin was the colloquial form spoken during the same time and attested in inscriptions and the works of comic playwrights like Plautus and Terence. Late Latin is the language from the 3rd century. Later, Early Modern Latin and Modern Latin evolved, Latin was used as the language of international communication, scholarship, and science until well into the 18th century, when it began to be supplanted by vernaculars. Ecclesiastical Latin remains the language of the Holy See and the Roman Rite of the Catholic Church. Today, many students, scholars and members of the Catholic clergy speak Latin fluently and it is taught in primary, secondary and postsecondary educational institutions around the world. The language has been passed down through various forms, some inscriptions have been published in an internationally agreed, monumental, multivolume series, the Corpus Inscriptionum Latinarum. Authors and publishers vary, but the format is about the same, volumes detailing inscriptions with a critical apparatus stating the provenance, the reading and interpretation of these inscriptions is the subject matter of the field of epigraphy. The works of several hundred ancient authors who wrote in Latin have survived in whole or in part and they are in part the subject matter of the field of classics. The Cat in the Hat, and a book of fairy tales, additional resources include phrasebooks and resources for rendering everyday phrases and concepts into Latin, such as Meissners Latin Phrasebook. The Latin influence in English has been significant at all stages of its insular development. From the 16th to the 18th centuries, English writers cobbled together huge numbers of new words from Latin and Greek words, dubbed inkhorn terms, as if they had spilled from a pot of ink. Many of these words were used once by the author and then forgotten, many of the most common polysyllabic English words are of Latin origin through the medium of Old French. Romance words make respectively 59%, 20% and 14% of English, German and those figures can rise dramatically when only non-compound and non-derived words are included. Accordingly, Romance words make roughly 35% of the vocabulary of Dutch, Roman engineering had the same effect on scientific terminology as a whole
10.
Binary number
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The base-2 system is a positional notation with a radix of 2. Because of its implementation in digital electronic circuitry using logic gates. Each digit is referred to as a bit, the modern binary number system was devised by Gottfried Leibniz in 1679 and appears in his article Explication de lArithmétique Binaire. Systems related to binary numbers have appeared earlier in multiple cultures including ancient Egypt, China, Leibniz was specifically inspired by the Chinese I Ching. The scribes of ancient Egypt used two different systems for their fractions, Egyptian fractions and Horus-Eye fractions, the method used for ancient Egyptian multiplication is also closely related to binary numbers. This method can be seen in use, for instance, in the Rhind Mathematical Papyrus, the I Ching dates from the 9th century BC in China. The binary notation in the I Ching is used to interpret its quaternary divination technique and it is based on taoistic duality of yin and yang. Eight trigrams and a set of 64 hexagrams, analogous to the three-bit and six-bit binary numerals, were in use at least as early as the Zhou Dynasty of ancient China. The Song Dynasty scholar Shao Yong rearranged the hexagrams in a format that resembles modern binary numbers, the Indian scholar Pingala developed a binary system for describing prosody. He used binary numbers in the form of short and long syllables, Pingalas Hindu classic titled Chandaḥśāstra describes the formation of a matrix in order to give a unique value to each meter. The binary representations in Pingalas system increases towards the right, the residents of the island of Mangareva in French Polynesia were using a hybrid binary-decimal system before 1450. Slit drums with binary tones are used to encode messages across Africa, sets of binary combinations similar to the I Ching have also been used in traditional African divination systems such as Ifá as well as in medieval Western geomancy. The base-2 system utilized in geomancy had long been applied in sub-Saharan Africa. Leibnizs system uses 0 and 1, like the modern binary numeral system, Leibniz was first introduced to the I Ching through his contact with the French Jesuit Joachim Bouvet, who visited China in 1685 as a missionary. Leibniz saw the I Ching hexagrams as an affirmation of the universality of his own beliefs as a Christian. Binary numerals were central to Leibnizs theology and he believed that binary numbers were symbolic of the Christian idea of creatio ex nihilo or creation out of nothing. Is not easy to impart to the pagans, is the ex nihilo through Gods almighty power. In 1854, British mathematician George Boole published a paper detailing an algebraic system of logic that would become known as Boolean algebra
11.
Ternary numeral system
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The ternary numeral system has three as its base. Analogous to a bit, a digit is a trit. One trit is equivalent to bits of information. Representations of integer numbers in ternary do not get uncomfortably lengthy as quickly as in binary, for example, decimal 365 corresponds to binary 101101101 and to ternary 111112. However, they are far less compact than the corresponding representations in bases such as decimal – see below for a compact way to codify ternary using nonary. The value of a number with n bits that are all 1 is 2n −1. Then N = M, N = /, and N = bd −1, for a three-digit ternary number, N =33 −1 =26 =2 ×32 +2 ×31 +2 ×30 =18 +6 +2. Nonary or septemvigesimal can be used for representation of ternary. A base-three system is used in Islam to keep track of counting Tasbih to 99 or to 100 on a hand for counting prayers. In certain analog logic, the state of the circuit is often expressed ternary and this is most commonly seen in Transistor–transistor logic using 7406 open collector logic. The output is said to either be low, high, or open, in this configuration the output of the circuit is actually not connected to any voltage reference at all. Where the signal is usually grounded to a reference, or at a certain voltage level. Thus, the voltage level is sometimes unpredictable. A rare ternary point is used to denote fractional parts of an inning in baseball, since each inning consists of three outs, each out is considered one third of an inning and is denoted as.1. For example, if a player pitched all of the 4th, 5th and 6th innings, plus 2 outs of the 7th inning, his Innings pitched column for that game would be listed as 3.2, meaning 3⅔. In this usage, only the part of the number is written in ternary form. Ternary numbers can be used to convey self-similar structures like the Sierpinski triangle or the Cantor set conveniently, additionally, it turns out that the ternary representation is useful for defining the Cantor set and related point sets, because of the way the Cantor set is constructed. The Cantor set consists of the points from 0 to 1 that have an expression that does not contain any instance of the digit 1
12.
Quaternary numeral system
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Quaternary is the base-4 numeral system. It uses the digits 0,1,2 and 3 to represent any real number. Four is the largest number within the range and one of two numbers that is both a square and a highly composite number, making quaternary a convenient choice for a base at this scale. Despite being twice as large, its economy is equal to that of binary. However, it no better in the localization of prime numbers. See decimal and binary for a discussion of these properties, as with the octal and hexadecimal numeral systems, quaternary has a special relation to the binary numeral system. Each radix 4,8 and 16 is a power of 2, so the conversion to and from binary is implemented by matching each digit with 2,3 or 4 binary digits, for example, in base 4,302104 =11001001002. Although octal and hexadecimal are widely used in computing and computer programming in the discussion and analysis of binary arithmetic and logic, by analogy with byte and nybble, a quaternary digit is sometimes called a crumb. There is a surviving list of Ventureño language number words up to 32 written down by a Spanish priest ca, the Kharosthi numerals have a partial base 4 counting system from 1 to decimal 10. Quaternary numbers are used in the representation of 2D Hilbert curves, here a real number between 0 and 1 is converted into the quaternary system. Every single digit now indicates in which of the respective 4 sub-quadrants the number will be projected, parallels can be drawn between quaternary numerals and the way genetic code is represented by DNA. The four DNA nucleotides in order, abbreviated A, C, G and T, can be taken to represent the quaternary digits in numerical order 0,1,2. With this encoding, the complementary digit pairs 0↔3, and 1↔2 match the complementation of the pairs, A↔T and C↔G. For example, the nucleotide sequence GATTACA can be represented by the quaternary number 2033010, quaternary line codes have been used for transmission, from the invention of the telegraph to the 2B1Q code used in modern ISDN circuits
13.
Quinary
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Quinary is a numeral system with five as the base. A possible origination of a system is that there are five fingers on either hand. The base five is stated from 0–4, in the quinary place system, five numerals, from 0 to 4, are used to represent any real number. According to this method, five is written as 10, twenty-five is written as 100, today, the main usage of base 5 is as a biquinary system, which is decimal using five as a sub-base. Another example of a system, is sexagesimal, base 60. Each quinary digit has log25 bits of information, many languages use quinary number systems, including Gumatj, Nunggubuyu, Kuurn Kopan Noot, Luiseño and Saraveca. Gumatj is a true 5–25 language, in which 25 is the group of 5. The Gumatj numerals are shown below, In the video game Riven and subsequent games of the Myst franchise, a decimal system with 2 and 5 as a sub-bases is called biquinary, and is found in Wolof and Khmer. Roman numerals are a biquinary system, the numbers 1,5,10, and 50 are written as I, V, X, and L respectively. Eight is VIII and seventy is LXX, most versions of the abacus use a biquinary system to simulate a decimal system for ease of calculation. Urnfield culture numerals and some tally mark systems are also biquinary, units of currencies are commonly partially or wholly biquinary. A vigesimal system with 4 and 5 as a sub-bases is found in Nahuatl, pentimal system Quibinary Yan Tan Tethera References, Quinary Base Conversion, includes fractional part, from Math Is Fun Media related to Quinary numeral system at Wikimedia Commons
14.
Senary
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The senary numeral system has six as its base. It has been adopted independently by a number of cultures. Like decimal, it is a semiprime, though being the product of the two consecutive numbers that are both prime it has a high degree of mathematical properties for its size. As six is a highly composite number, many of the arguments made in favor of the duodecimal system also apply to this base-6. Senary may be considered interesting in the study of numbers, since all primes other than 2 and 3. That is, for every number p greater than 3, one has the modular arithmetic relations that either p ≡1 or 5. This property maximizes the probability that the result of an integer multiplication will end in zero, E. g. if three fingers are extended on the left hand and four on the right, 34senary is represented. This is equivalent to 3 ×6 +4 which is 22decimal, flipping the sixes hand around to its backside may help to further disambiguate which hand represents the sixes and which represents the units. While most developed cultures count by fingers up to 5 in very similar ways, beyond 5 non-Western cultures deviate from Western methods, such as with Chinese number gestures. More abstract finger counting systems, such as chisanbop or finger binary, allow counting to 99,1,023, or even higher depending on the method. The English monk and historian Bede, in the first chapter of De temporum ratione, titled Tractatus de computo, vel loquela per gestum digitorum, the Ndom language of Papua New Guinea is reported to have senary numerals. Mer means 6, mer an thef means 6 ×2 =12, nif means 36, another example from Papua New Guinea are the Morehead-Maro languages. In these languages, counting is connected to ritualized yam-counting and these languages count from a base six, employing words for the powers of six, running up to 66 for some of the languages. One example is Kómnzo with the numerals, nimbo, féta, tarumba, ntamno, wärämäkä. Some Niger-Congo languages have been reported to use a number system, usually in addition to another. For some purposes, base 6 might be too small a base for convenience. The choice of 36 as a radix is convenient in that the digits can be represented using the Arabic numerals 0–9 and the Latin letters A–Z, this choice is the basis of the base36 encoding scheme. Base36 encoding scheme Binary Ternary Duodecimal Sexagesimal Shacks Base Six Dialectic Digital base 6 clock Analog Clock Designer capable of rendering a base 6 clock Senary base conversion
15.
Octal
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The octal numeral system, or oct for short, is the base-8 number system, and uses the digits 0 to 7. Octal numerals can be made from binary numerals by grouping binary digits into groups of three. For example, the representation for decimal 74 is 1001010. Two zeroes can be added at the left,1001010, corresponding the octal digits 112, in the decimal system each decimal place is a power of ten. For example,7410 =7 ×101 +4 ×100 In the octal system each place is a power of eight. The Yuki language in California and the Pamean languages in Mexico have octal systems because the speakers count using the spaces between their fingers rather than the fingers themselves and it has been suggested that the reconstructed Proto-Indo-European word for nine might be related to the PIE word for new. Based on this, some have speculated that proto-Indo-Europeans used a number system. In 1716 King Charles XII of Sweden asked Emanuel Swedenborg to elaborate a number based on 64 instead of 10. Swedenborg however argued that for people with less intelligence than the king such a big base would be too difficult, in 1718 Swedenborg wrote a manuscript, En ny rekenkonst som om vexlas wid Thalet 8 i stelle then wanliga wid Thalet 10. The numbers 1-7 are there denoted by the l, s, n, m, t, f, u. Thus 8 = lo,16 = so,24 = no,64 = loo,512 = looo etc, numbers with consecutive consonants are pronounced with vowel sounds between in accordance with a special rule. Writing under the pseudonym Hirossa Ap-Iccim in The Gentlemans Magazine, July 1745, Hugh Jones proposed a system for British coins, weights. In 1801, James Anderson criticized the French for basing the Metric system on decimal arithmetic and he suggested base 8 for which he coined the term octal. In the mid 19th century, Alfred B. Taylor concluded that Our octonary radix is, therefore, so, for example, the number 65 would be spoken in octonary as under-un. Taylor also republished some of Swedenborgs work on octonary as an appendix to the above-cited publications, in the 2009 film Avatar, the language of the extraterrestrial Navi race employs an octal numeral system, probably due to the fact that they have four fingers on each hand. In the TV series Stargate SG-1, the Ancients, a race of beings responsible for the invention of the Stargates, in the tabletop game series Warhammer 40,000, the Tau race use an octal number system. Octal became widely used in computing systems such as the PDP-8, ICL1900. Octal was an abbreviation of binary for these machines because their word size is divisible by three
16.
Duodecimal
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The duodecimal system is a positional notation numeral system using twelve as its base. In this system, the number ten may be written by a rotated 2 and this notation was introduced by Sir Isaac Pitman. These digit forms are available as Unicode characters on computerized systems since June 2015 as ↊ and ↋, other notations use A, T, or X for ten and B or E for eleven. The number twelve is written as 10 in duodecimal, whereas the digit string 12 means 1 dozen and 2 units. Similarly, in duodecimal 100 means 1 gross,1000 means 1 great gross, the number twelve, a superior highly composite number, is the smallest number with four non-trivial factors, and the smallest to include as factors all four numbers within the subitizing range. As a result, duodecimal has been described as the number system. Of its factors,2 and 3 are prime, which means the reciprocals of all 3-smooth numbers have a representation in duodecimal. In particular, the five most elementary fractions all have a terminating representation in duodecimal. This all makes it a convenient number system for computing fractions than most other number systems in common use, such as the decimal, vigesimal, binary. Although the trigesimal and sexagesimal systems do even better in respect, this is at the cost of unwieldy multiplication tables. In this section, numerals are based on decimal places, for example,10 means ten,12 means twelve. Languages using duodecimal number systems are uncommon, germanic languages have special words for 11 and 12, such as eleven and twelve in English. However, they are considered to come from Proto-Germanic *ainlif and *twalif, historically, units of time in many civilizations are duodecimal. There are twelve signs of the zodiac, twelve months in a year, traditional Chinese calendars, clocks, and compasses are based on the twelve Earthly Branches. There are 12 inches in a foot,12 troy ounces in a troy pound,12 old British pence in a shilling,24 hours in a day. The Romans used a system based on 12, including the uncia which became both the English words ounce and inch. The importance of 12 has been attributed to the number of cycles in a year. It is possible to count to 12 with the acting as a pointer
17.
Hexadecimal
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In mathematics and computing, hexadecimal is a positional numeral system with a radix, or base, of 16. It uses sixteen distinct symbols, most often the symbols 0–9 to represent values zero to nine, Hexadecimal numerals are widely used by computer system designers and programmers. As each hexadecimal digit represents four binary digits, it allows a more human-friendly representation of binary-coded values, one hexadecimal digit represents a nibble, which is half of an octet or byte. For example, a byte can have values ranging from 00000000 to 11111111 in binary form. In a non-programming context, a subscript is typically used to give the radix, several notations are used to support hexadecimal representation of constants in programming languages, usually involving a prefix or suffix. The prefix 0x is used in C and related languages, where this value might be denoted as 0x2AF3, in contexts where the base is not clear, hexadecimal numbers can be ambiguous and confused with numbers expressed in other bases. There are several conventions for expressing values unambiguously, a numerical subscript can give the base explicitly,15910 is decimal 159,15916 is hexadecimal 159, which is equal to 34510. Some authors prefer a text subscript, such as 159decimal and 159hex, or 159d and 159h. example. com/name%20with%20spaces where %20 is the space character, thus ’, represents the right single quotation mark, Unicode code point number 2019 in hex,8217. In the Unicode standard, a value is represented with U+ followed by the hex value. Color references in HTML, CSS and X Window can be expressed with six hexadecimal digits prefixed with #, white, CSS allows 3-hexdigit abbreviations with one hexdigit per component, #FA3 abbreviates #FFAA33. *nix shells, AT&T assembly language and likewise the C programming language, to output an integer as hexadecimal with the printf function family, the format conversion code %X or %x is used. In Intel-derived assembly languages and Modula-2, hexadecimal is denoted with a suffixed H or h, some assembly languages use the notation HABCD. Ada and VHDL enclose hexadecimal numerals in based numeric quotes, 16#5A3#, for bit vector constants VHDL uses the notation x5A3. Verilog represents hexadecimal constants in the form 8hFF, where 8 is the number of bits in the value, the Smalltalk language uses the prefix 16r, 16r5A3 PostScript and the Bourne shell and its derivatives denote hex with prefix 16#, 16#5A3. For PostScript, binary data can be expressed as unprefixed consecutive hexadecimal pairs, in early systems when a Macintosh crashed, one or two lines of hexadecimal code would be displayed under the Sad Mac to tell the user what went wrong. Common Lisp uses the prefixes #x and #16r, setting the variables *read-base* and *print-base* to 16 can also used to switch the reader and printer of a Common Lisp system to Hexadecimal number representation for reading and printing numbers. Thus Hexadecimal numbers can be represented without the #x or #16r prefix code, MSX BASIC, QuickBASIC, FreeBASIC and Visual Basic prefix hexadecimal numbers with &H, &H5A3 BBC BASIC and Locomotive BASIC use & for hex. TI-89 and 92 series uses a 0h prefix, 0h5A3 ALGOL68 uses the prefix 16r to denote hexadecimal numbers, binary, quaternary and octal numbers can be specified similarly
18.
Vigesimal
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The vigesimal or base 20 numeral system is based on twenty. In a vigesimal system, twenty individual numerals are used. One modern method of finding the extra needed symbols is to write ten as the letter A20, to write nineteen as J20, and this is similar to the common computer-science practice of writing hexadecimal numerals over 9 with the letters A–F. Another method skips over the letter I, in order to avoid confusion between I20 as eighteen and one, so that the number eighteen is written as J20, the number twenty is written as 1020. According to this notation,2020 means forty in decimal = + D020 means two hundred and sixty in decimal = +10020 means four hundred in decimal = + +, in the rest of this article below, numbers are expressed in decimal notation, unless specified otherwise. For example,10 means ten,20 means twenty, in decimal, dividing by three twice only gives one digit periods because 9 is the number below ten. 21, however, the adjacent to 20 that is divisible by 3, is not divisible by 9. Ninths in vigesimal have six-digit periods, the prime factorization of twenty is 22 ×5, so it is not a perfect power. However, its part,5, is congruent to 1. Thus, according to Artins conjecture on primitive roots, vigesimal has infinitely many cyclic primes, but the fraction of primes that are cyclic is not necessarily ~37. 395%. An UnrealScript program that computes the lengths of recurring periods of various fractions in a set of bases found that, of the first 15,456 primes. In many European languages,20 is used as a base, vigesimal systems are common in Africa, for example in Yoruba. Ogún,20, is the basic numeric block, ogójì,40, =20 multiplied by 2. Ogota,60, =20 multiplied by 3, ogorin,80, =20 multiplied by 4. Ogorun,100, =20 multiplied by 5, twenty was a base in the Maya and Aztec number systems. The Maya used the names for the powers of twenty, kal, bak, pic, calab, kinchil. See also Maya numerals and Maya calendar, Mayan languages, Yucatec, the Aztec called them, cempoalli, centzontli, cenxiquipilli, cempoalxiquipilli, centzonxiquipilli and cempoaltzonxiquipilli. Note that the ce prefix at the beginning means one and is replaced with the number to get the names of other multiples of the power
19.
Base 36
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The senary numeral system has six as its base. It has been adopted independently by a number of cultures. Like decimal, it is a semiprime, though being the product of the two consecutive numbers that are both prime it has a high degree of mathematical properties for its size. As six is a highly composite number, many of the arguments made in favor of the duodecimal system also apply to this base-6. Senary may be considered interesting in the study of numbers, since all primes other than 2 and 3. That is, for every number p greater than 3, one has the modular arithmetic relations that either p ≡1 or 5. This property maximizes the probability that the result of an integer multiplication will end in zero, E. g. if three fingers are extended on the left hand and four on the right, 34senary is represented. This is equivalent to 3 ×6 +4 which is 22decimal, flipping the sixes hand around to its backside may help to further disambiguate which hand represents the sixes and which represents the units. While most developed cultures count by fingers up to 5 in very similar ways, beyond 5 non-Western cultures deviate from Western methods, such as with Chinese number gestures. More abstract finger counting systems, such as chisanbop or finger binary, allow counting to 99,1,023, or even higher depending on the method. The English monk and historian Bede, in the first chapter of De temporum ratione, titled Tractatus de computo, vel loquela per gestum digitorum, the Ndom language of Papua New Guinea is reported to have senary numerals. Mer means 6, mer an thef means 6 ×2 =12, nif means 36, another example from Papua New Guinea are the Morehead-Maro languages. In these languages, counting is connected to ritualized yam-counting and these languages count from a base six, employing words for the powers of six, running up to 66 for some of the languages. One example is Kómnzo with the numerals, nimbo, féta, tarumba, ntamno, wärämäkä. Some Niger-Congo languages have been reported to use a number system, usually in addition to another. For some purposes, base 6 might be too small a base for convenience. The choice of 36 as a radix is convenient in that the digits can be represented using the Arabic numerals 0–9 and the Latin letters A–Z, this choice is the basis of the base36 encoding scheme. Base36 encoding scheme Binary Ternary Duodecimal Sexagesimal Shacks Base Six Dialectic Digital base 6 clock Analog Clock Designer capable of rendering a base 6 clock Senary base conversion
20.
Urdu numerals
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These numbers are known as أرقام هندية in Arabic. They are sometimes also called Indic numerals in English, however, that is sometimes discouraged as it can lead to confusion with Indian numerals, used in Brahmic scripts of India. Each numeral in the Persian variant has a different Unicode point even if it looks identical to the Eastern Arabic numeral counterpart, however the variants used with Urdu, Sindhi and other South Asian languages are not encoded separately from the Persian variants. See U+0660 through U+0669 and U+06F0 through U+06F9, written numerals are arranged with their lowest-value digit to the right, with higher value positions added to the left. That is identical to the arrangement used by Western texts using Hindu-Arabic numerals even though Arabic script is read from right to left. There is no conflict unless numerical layout is necessary, as is the case for arithmetic problems and lists of numbers, Eastern Arabic numerals remain strongly predominant vis-à-vis Western Arabic numerals in many countries to the East of the Arab world, particularly in Iran and Afghanistan. In Pakistan, Western Arabic numerals are more used as a considerable majority of the population is anglophone. Eastern numerals still continue to see use in Urdu publications and newspapers, in North Africa, only Western Arabic numerals are now commonly used. In medieval times, these used a slightly different set
21.
Tamil numerals
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Traditionally Vattezhuttu characters were used, but now Arabic numerals have become commonplace. Old Tamil possesses a special character for zero and it is read as andru. But yet Modern Tamil renounces the use of its native character, Modern Tamil words for zero include சுழியம் or பூச்சியம். Tamil has a prefix for each number from 1 to 9. For instance, the word for fifty, ஐம்பது is a combination of ஐ, the prefix for nine changes with respect to the succeeding base 10. தொ+ the unvoiced consonant of the succeeding base 10 forms the prefix for nine, for instance,90 is தொ+ண், hence, தொண்ணூறு). These are typically void in the Tamil language except for some Hindu and Christian religious references, example அட்ட இலட்சுமிகள் in a Hindu context, unlike other Indian languages, Tamil has distinct digits for 10,100, and 1000. It also has characters for other number-based aspects of day-to-day life. − − − − − − − − − − − − There are two systems that can be used in the Tamil language, the Tamil system which is as follows. The following are the numbers of the Ancient Tamil Country. Sanskrit based multiples like lakhs are also followed just like other Indian languages and you can transcribe any fraction, by affixing -இல் after the denominator followed by the numerator. For instance, 1/41 can be said as நாற்பத்து ஒன்றில் ஒன்று, the suffixing of the -இல் requires you to change the last consonant of the number to its இ form. For example, மூன்று+இல் becomes மூன்றில், note the உ has been omitted, common fractions have names already allocated to them, hence, these names are often used rather than the above method. Other fractions are, Anu was considered as lowest fraction by ancient Tamils as size of smallest physical object, later, this term went to Sanskrit to refer directly atom. Decimal point is called புள்ளி in Tamil, for example,1.1 would be read as ஒன்று புள்ளி ஒன்று. Percentage is known as விழுக்காடு in Tamil or சதவீதம் and these words are simply added after a number to form percentages. For instance, four percent is நான்கு சதவீதம் or நான்கு விழுக்காடு, percentage symbol is also recognised and used. Ordinal numbers are formed by adding the suffix -ஆம் after the number, as always, when blending two words into one, an unvoiced form of the consonant as the one that the second starts with, is placed in between to blend
22.
Natural number
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In mathematics, the natural numbers are those used for counting and ordering. In common language, words used for counting are cardinal numbers, texts that exclude zero from the natural numbers sometimes refer to the natural numbers together with zero as the whole numbers, but in other writings, that term is used instead for the integers. These chains of extensions make the natural numbers canonically embedded in the number systems. Properties of the numbers, such as divisibility and the distribution of prime numbers, are studied in number theory. Problems concerning counting and ordering, such as partitioning and enumerations, are studied in combinatorics, the most primitive method of representing a natural number is to put down a mark for each object. Later, a set of objects could be tested for equality, excess or shortage, by striking out a mark, the first major advance in abstraction was the use of numerals to represent numbers. This allowed systems to be developed for recording large numbers, the ancient Egyptians developed a powerful system of numerals with distinct hieroglyphs for 1,10, and all the powers of 10 up to over 1 million. A stone carving from Karnak, dating from around 1500 BC and now at the Louvre in Paris, depicts 276 as 2 hundreds,7 tens, and 6 ones, and similarly for the number 4,622. A much later advance was the development of the idea that 0 can be considered as a number, with its own numeral. The use of a 0 digit in place-value notation dates back as early as 700 BC by the Babylonians, the Olmec and Maya civilizations used 0 as a separate number as early as the 1st century BC, but this usage did not spread beyond Mesoamerica. The use of a numeral 0 in modern times originated with the Indian mathematician Brahmagupta in 628, the first systematic study of numbers as abstractions is usually credited to the Greek philosophers Pythagoras and Archimedes. Some Greek mathematicians treated the number 1 differently than larger numbers, independent studies also occurred at around the same time in India, China, and Mesoamerica. In 19th century Europe, there was mathematical and philosophical discussion about the nature of the natural numbers. A school of Naturalism stated that the numbers were a direct consequence of the human psyche. Henri Poincaré was one of its advocates, as was Leopold Kronecker who summarized God made the integers, in opposition to the Naturalists, the constructivists saw a need to improve the logical rigor in the foundations of mathematics. In the 1860s, Hermann Grassmann suggested a recursive definition for natural numbers thus stating they were not really natural, later, two classes of such formal definitions were constructed, later, they were shown to be equivalent in most practical applications. The second class of definitions was introduced by Giuseppe Peano and is now called Peano arithmetic and it is based on an axiomatization of the properties of ordinal numbers, each natural number has a successor and every non-zero natural number has a unique predecessor. Peano arithmetic is equiconsistent with several systems of set theory
23.
English-speaking countries
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Approximately 330 to 360 million people speak English as their first language. More than half of live in the United States, followed by some 55 million in England. English is the third largest language by number of speakers, after Mandarin. Estimates that include second language speakers vary greatly, from 470 million to more than 1 billion, david Crystal calculates that non-native speakers as of 2003 outnumbered native speakers by a ratio of 3 to 1. When combining native and non-native speakers, English is the most widely spoken language worldwide, there are six large countries with a majority of native English speakers that are sometimes grouped under the term Anglosphere. They are, in descending order of English speakers, the United States, the United Kingdom, Canada, Australia, Ireland, other substantial communities of native speakers are found in South Africa, and Nigeria. Also there are countries where in a part of the territory English became a language, e. g. Colombias San Andrés y Providencia. This was a result of the influence of British colonization in the area, English is one of the eleven official languages that are given equal status in South Africa. It is also the language in current dependent territories of Australia and of the United States. Although the United States federal government has no official languages, English has been official status by 32 of the 50 state governments. It is, by treaty, the official language for aeronautical. English is one of the languages of the United Nations and many other international organizations. In 2012, excluding native speakers,38 percent of Europeans consider that they can speak English, in publishing, English literature predominates considerably with 28 percent of all books published in the world and 30 percent of web content in 2011. This increasing use of the English language globally has had a impact on many other languages, leading to language shift and even language death. English itself has more open to language shift as multiple regional varieties feed back into the language as a whole. Variation in Nonnative Varieties of English, Northern Ireland Statistics and Research Agency. Census 2011, Key Statistics for Northern Ireland December 2012, language in England and Wales,2011. Language Use in the United States,2011, Population by mother tongue and age groups,2011 counts, for Canada, provinces and territories
24.
Decimal mark
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A decimal mark is a symbol used to separate the integer part from the fractional part of a number written in decimal form. Different countries officially designate different symbols for the decimal mark, the choice of symbol for the decimal mark also affects the choice of symbol for the thousands separator used in digit grouping, so the latter is also treated in this article. In mathematics the decimal mark is a type of radix point, in the Middle Ages, before printing, a bar over the units digit was used to separate the integral part of a number from its fractional part, e. g.9995. His Compendious Book on Calculation by Completion and Balancing presented the first systematic solution of linear, a similar notation remains in common use as an underbar to superscript digits, especially for monetary values without a decimal mark, e. g.9995. Later, a separatrix between the units and tenths position became the norm among Arab mathematicians, e. g. 99ˌ95, when this character was typeset, it was convenient to use the existing comma or full stop instead. The separatrix was also used in England as an L-shaped or vertical bar before the popularization of the period, gerbert of Aurillac marked triples of columns with an arc when using his Hindu–Arabic numeral-based abacus in the 10th century. Fibonacci followed this convention when writing numbers such as in his influential work Liber Abaci in the 13th century, in France, the full stop was already in use in printing to make Roman numerals more readable, so the comma was chosen. Many other countries, such as Italy, also chose to use the comma to mark the decimal units position and it has been made standard by the ISO for international blueprints. However, English-speaking countries took the comma to separate sequences of three digits, in some countries, a raised dot or dash may be used for grouping or decimal mark, this is particularly common in handwriting. In the United States, the stop or period was used as the standard decimal mark. g. However, as the mid dot was already in use in the mathematics world to indicate multiplication. In the event, the point was decided on by the Ministry of Technology in 1968, the three most spoken international auxiliary languages, Ido, Esperanto, and Interlingua, all use the comma as the decimal mark. Interlingua has used the comma as its decimal mark since the publication of the Interlingua Grammar in 1951, Esperanto also uses the comma as its official decimal mark, while thousands are separated by non-breaking spaces,12345678,9. Idos Kompleta Gramatiko Detaloza di la Linguo Internaciona Ido officially states that commas are used for the mark while full stops are used to separate thousands, millions. So the number 12,345,678.90123 for instance, the 1931 grammar of Volapük by Arie de Jong uses the comma as its decimal mark, and uses the middle dot as the thousands separator. In 1958, disputes between European and American delegates over the representation of the decimal mark nearly stalled the development of the ALGOL computer programming language. ALGOL ended up allowing different decimal marks, but most computer languages, the 22nd General Conference on Weights and Measures declared in 2003 that the symbol for the decimal marker shall be either the point on the line or the comma on the line. It further reaffirmed that numbers may be divided in groups of three in order to facilitate reading, neither dots nor commas are ever inserted in the spaces between groups
25.
Germanic languages
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It is the third most spoken Indo-European subdivision, behind Italic and Indo-Iranian, and ahead of Balto-Slavic languages. Limburgish varieties have roughly 1.3 million speakers along the Dutch–Belgian–German border, the main North Germanic languages are Norwegian, Danish, Swedish, Icelandic, and Faroese, which have a combined total of about 20 million speakers. The East Germanic branch included Gothic, Burgundian, and Vandalic, the last to die off was Crimean Gothic, spoken in the late 18th century in some isolated areas of Crimea. The total number of Germanic languages throughout history is unknown, as some of them—especially East Germanic languages—disappeared during or after the Migration Period. Proto-Germanic, along all of its descendants, is characterized by a number of unique linguistic features. Early varieties of Germanic enter history with the Germanic tribes moving south from Scandinavia in the 2nd century BC, to settle in the area of todays northern Germany, furthermore, it is the de facto language of the United Kingdom, the United States and Australia. It is also a language in Nicaragua and Malaysia. German is a language of Austria, Belgium, Germany, Liechtenstein, Luxembourg and Switzerland and has regional status in Italy, Poland, Namibia. German also continues to be spoken as a minority language by immigrant communities in North America, South America, Central America, Mexico, a German dialect, Pennsylvania Dutch, is still present amongst Anabaptist populations in Pennsylvania in the United States. Dutch is a language of Aruba, Belgium, Curaçao. The Netherlands also colonised Indonesia, but Dutch was scrapped as a language after Indonesian independence. Dutch was until 1925 an official language in South Africa, but evolved in and was replaced by Afrikaans, Afrikaans is one of the 11 official languages in South Africa and is a lingua franca of Namibia. It is used in other Southern African nations as well, low German is a collection of sometimes very diverse dialects spoken in the northeast of the Netherlands and northern Germany. Scots is spoken in Lowland Scotland and parts of Ulster, frisian is spoken among half a million people who live on the southern fringes of the North Sea in the Netherlands, Germany, and Denmark. Luxembourgish is mainly spoken in the Grand Duchy of Luxembourg, though it extends into small parts of Belgium, France. Limburgish varieties are spoken in the Limburg and Rhineland regions, along the Dutch–Belgian–German border, Swedish is also one of the two official languages in Finland, along with Finnish, and the only official language in the Åland Islands. Danish is also spoken natively by the Danish minority in the German state of Schleswig-Holstein, Norwegian is the official language of Norway. Icelandic is the language of Iceland, and is spoken by a significant minority in the Faroe Islands
26.
1 (number)
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1, is a number, a numeral, and the name of the glyph representing that number. It represents a single entity, the unit of counting or measurement, for example, a line segment of unit length is a line segment of length 1. It is also the first of the series of natural numbers. The word one can be used as a noun, an adjective and it comes from the English word an, which comes from the Proto-Germanic root *ainaz. The Proto-Germanic root *ainaz comes from the Proto-Indo-European root *oi-no-, compare the Proto-Germanic root *ainaz to Old Frisian an, Gothic ains, Danish een, Dutch een, German eins and Old Norse einn. Compare the Proto-Indo-European root *oi-no- to Greek oinos, Latin unus, Old Persian aivam, Old Church Slavonic -inu and ino-, Lithuanian vienas, Old Irish oin, One, sometimes referred to as unity, is the first non-zero natural number. It is thus the integer before two and after zero, and the first positive odd number, any number multiplied by one is that number, as one is the identity for multiplication. As a result,1 is its own factorial, its own square, its own cube, One is also the result of the empty product, as any number multiplied by one is itself. It is also the natural number that is neither composite nor prime with respect to division. The Gupta wrote it as a line, and the Nagari sometimes added a small circle on the left. The Nepali also rotated it to the right but kept the circle small and this eventually became the top serif in the modern numeral, but the occasional short horizontal line at the bottom probably originates from similarity with the Roman numeral I. Where the 1 is written with an upstroke, the number 7 has a horizontal stroke through the vertical line. While the shape of the 1 character has an ascender in most modern typefaces, in typefaces with text figures, many older typewriters do not have a separate symbol for 1 and use the lowercase letter l instead. It is possible to find cases when the uppercase J is used,1 cannot be used as the base of a positional numeral system, as the only digit that would be permitted in such a system would be 0. Since the base 1 exponential function always equals 1, its inverse does not exist, there are two ways to write the real number 1 as a recurring decimal, as 1.000. and as 0.999. There is only one way to represent the real number 1 as a Dedekind cut, in a multiplicative group or monoid, the identity element is sometimes denoted 1, but e is also traditional. However,1 is especially common for the identity of a ring. When such a ring has characteristic n not equal to 0,1 is the first figurate number of every kind, such as triangular number, pentagonal number and centered hexagonal number, to name just a few
27.
0 (number)
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0 is both a number and the numerical digit used to represent that number in numerals. The number 0 fulfills a role in mathematics as the additive identity of the integers, real numbers. As a digit,0 is used as a placeholder in place value systems, names for the number 0 in English include zero, nought or naught, nil, or—in contexts where at least one adjacent digit distinguishes it from the letter O—oh or o. Informal or slang terms for zero include zilch and zip, ought and aught, as well as cipher, have also been used historically. The word zero came into the English language via French zéro from Italian zero, in pre-Islamic time the word ṣifr had the meaning empty. Sifr evolved to mean zero when it was used to translate śūnya from India, the first known English use of zero was in 1598. The Italian mathematician Fibonacci, who grew up in North Africa and is credited with introducing the system to Europe. This became zefiro in Italian, and was contracted to zero in Venetian. The Italian word zefiro was already in existence and may have influenced the spelling when transcribing Arabic ṣifr, modern usage There are different words used for the number or concept of zero depending on the context. For the simple notion of lacking, the words nothing and none are often used, sometimes the words nought, naught and aught are used. Several sports have specific words for zero, such as nil in football, love in tennis and it is often called oh in the context of telephone numbers. Slang words for zero include zip, zilch, nada, duck egg and goose egg are also slang for zero. Ancient Egyptian numerals were base 10 and they used hieroglyphs for the digits and were not positional. By 1740 BC, the Egyptians had a symbol for zero in accounting texts. The symbol nfr, meaning beautiful, was used to indicate the base level in drawings of tombs and pyramids. By the middle of the 2nd millennium BC, the Babylonian mathematics had a sophisticated sexagesimal positional numeral system, the lack of a positional value was indicated by a space between sexagesimal numerals. By 300 BC, a symbol was co-opted as a placeholder in the same Babylonian system. In a tablet unearthed at Kish, the scribe Bêl-bân-aplu wrote his zeros with three hooks, rather than two slanted wedges, the Babylonian placeholder was not a true zero because it was not used alone
28.
Scientific notation
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Scientific notation is a way of expressing numbers that are too big or too small to be conveniently written in decimal form. It is commonly used by scientists, mathematicians and engineers, in part because it can simplify certain arithmetic operations, on scientific calculators it is known as SCI display mode. In scientific notation all numbers are written in the form m × 10n, where the exponent n is an integer, however, the term mantissa may cause confusion because it is the name of the fractional part of the common logarithm. If the number is then a minus sign precedes m. In normalized notation, the exponent is chosen so that the value of the coefficient is at least one. Decimal floating point is an arithmetic system closely related to scientific notation. Any given integer can be written in the form m×10^n in many ways, in normalized scientific notation, the exponent n is chosen so that the absolute value of m remains at least one but less than ten. Thus 350 is written as 3. 5×102 and this form allows easy comparison of numbers, as the exponent n gives the numbers order of magnitude. In normalized notation, the exponent n is negative for a number with absolute value between 0 and 1, the 10 and exponent are often omitted when the exponent is 0. Normalized scientific form is the form of expression of large numbers in many fields, unless an unnormalized form. Normalized scientific notation is often called exponential notation—although the latter term is general and also applies when m is not restricted to the range 1 to 10. Engineering notation differs from normalized scientific notation in that the exponent n is restricted to multiples of 3, consequently, the absolute value of m is in the range 1 ≤ |m| <1000, rather than 1 ≤ |m| <10. Though similar in concept, engineering notation is rarely called scientific notation, engineering notation allows the numbers to explicitly match their corresponding SI prefixes, which facilitates reading and oral communication. A significant figure is a digit in a number that adds to its precision and this includes all nonzero numbers, zeroes between significant digits, and zeroes indicated to be significant. Leading and trailing zeroes are not significant because they exist only to show the scale of the number. Therefore,1,230,400 usually has five significant figures,1,2,3,0, and 4, when a number is converted into normalized scientific notation, it is scaled down to a number between 1 and 10. All of the significant digits remain, but the place holding zeroes are no longer required, thus 1,230,400 would become 1.2304 ×106. However, there is also the possibility that the number may be known to six or more significant figures, thus, an additional advantage of scientific notation is that the number of significant figures is clearer
29.
SI prefix
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A metric prefix is a unit prefix that precedes a basic unit of measure to indicate a multiple or fraction of the unit. While all metric prefixes in use today are decadic, historically there have been a number of binary metric prefixes as well. Each prefix has a symbol that is prepended to the unit symbol. The prefix kilo-, for example, may be added to gram to indicate multiplication by one thousand, the prefix milli-, likewise, may be added to metre to indicate division by one thousand, one millimetre is equal to one thousandth of a metre. Decimal multiplicative prefixes have been a feature of all forms of the system with six dating back to the systems introduction in the 1790s. Metric prefixes have even been prepended to non-metric units, the SI prefixes are standardized for use in the International System of Units by the International Bureau of Weights and Measures in resolutions dating from 1960 to 1991. Since 2009, they have formed part of the International System of Quantities, the BIPM specifies twenty prefixes for the International System of Units. Each prefix name has a symbol which is used in combination with the symbols for units of measure. For example, the symbol for kilo- is k, and is used to produce km, kg, and kW, which are the SI symbols for kilometre, kilogram, prefixes corresponding to an integer power of one thousand are generally preferred. Hence 100 m is preferred over 1 hm or 10 dam, the prefixes hecto, deca, deci, and centi are commonly used for everyday purposes, and the centimetre is especially common. However, some building codes require that the millimetre be used in preference to the centimetre, because use of centimetres leads to extensive usage of decimal points. Prefixes may not be used in combination and this also applies to mass, for which the SI base unit already contains a prefix. For example, milligram is used instead of microkilogram, in the arithmetic of measurements having units, the units are treated as multiplicative factors to values. If they have prefixes, all but one of the prefixes must be expanded to their numeric multiplier,1 km2 means one square kilometre, or the area of a square of 1000 m by 1000 m and not 1000 square metres. 2 Mm3 means two cubic megametres, or the volume of two cubes of 1000000 m by 1000000 m by 1000000 m or 2×1018 m3, and not 2000000 cubic metres, examples 5 cm = 5×10−2 m =5 ×0.01 m =0. The prefixes, including those introduced after 1960, are used with any metric unit, metric prefixes may also be used with non-metric units. The choice of prefixes with a unit is usually dictated by convenience of use. Unit prefixes for amounts that are larger or smaller than those actually encountered are seldom used
30.
Number
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A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1,2,3, a notational symbol that represents a number is called a numeral. In addition to their use in counting and measuring, numerals are used for labels, for ordering. In common usage, number may refer to a symbol, a word, calculations with numbers are done with arithmetical operations, the most familiar being addition, subtraction, multiplication, division, and exponentiation. Their study or usage is called arithmetic, the same term may also refer to number theory, the study of the properties of numbers. Besides their practical uses, numbers have cultural significance throughout the world, for example, in Western society the number 13 is regarded as unlucky, and a million may signify a lot. Though it is now regarded as pseudoscience, numerology, the belief in a significance of numbers, permeated ancient. Numerology heavily influenced the development of Greek mathematics, stimulating the investigation of problems in number theory which are still of interest today. During the 19th century, mathematicians began to develop many different abstractions which share certain properties of numbers, among the first were the hypercomplex numbers, which consist of various extensions or modifications of the complex number system. Numbers should be distinguished from numerals, the used to represent numbers. Boyer showed that Egyptians created the first ciphered numeral system, Greeks followed by mapping their counting numbers onto Ionian and Doric alphabets. The number five can be represented by digit 5 or by the Roman numeral Ⅴ, notations used to represent numbers are discussed in the article numeral systems. The Roman numerals require extra symbols for larger numbers, different types of numbers have many different uses. Numbers can be classified into sets, called number systems, such as the natural numbers, the same number can be written in many different ways. For different methods of expressing numbers with symbols, such as the Roman numerals, each of these number systems may be considered as a proper subset of the next one. This is expressed, symbolically, by writing N ⊂ Z ⊂ Q ⊂ R ⊂ C, the most familiar numbers are the natural numbers,1,2,3, and so on. Traditionally, the sequence of numbers started with 1 However, in the 19th century, set theorists. Today, different mathematicians use the term to both sets, including 0 or not
31.
Numerical digit
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A digit is a numeric symbol used in combinations to represent numbers in positional numeral systems. The name digit comes from the fact that the 10 digits of the hands correspond to the 10 symbols of the common base 10 numeral system, i. e. the decimal digits. In a given system, if the base is an integer. For example, the system has ten digits, whereas binary has two digits. In a basic system, a numeral is a sequence of digits. Each position in the sequence has a value, and each digit has a value. The value of the numeral is computed by multiplying each digit in the sequence by its place value, each digit in a number system represents an integer. For example, in decimal the digit 1 represents the one, and in the hexadecimal system. A positional number system must have a digit representing the integers from zero up to, but not including, thus in the positional decimal system, the numbers 0 to 9 can be expressed using their respective numerals 0 to 9 in the rightmost units position. The Hindu–Arabic numeral system uses a decimal separator, commonly a period in English, or a comma in other European languages, to denote the place or units place. Each successive place to the left of this has a value equal to the place value of the previous digit times the base. Similarly, each place to the right of the separator has a place value equal to the place value of the previous digit divided by the base. For example, in the numeral 10, the total value of the number is 1 ten,0 ones,3 tenths, and 4 hundredths. Note that the zero, which contributes no value to the number, the place value of any given digit in a numeral can be given by a simple calculation, which in itself is a compliment to the logic behind numeral systems. And to the right, the digit is multiplied by the base raised by a negative n, for example, in the number 10. This system was established by the 7th century in India, but was not yet in its modern form because the use of the digit zero had not yet widely accepted. Instead of a zero, a dot was left in the numeral as a placeholder, the first widely acknowledged use of zero was in 876. The original numerals were very similar to the ones, even down to the glyphs used to represent digits
32.
Thousands separator
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A decimal mark is a symbol used to separate the integer part from the fractional part of a number written in decimal form. Different countries officially designate different symbols for the decimal mark, the choice of symbol for the decimal mark also affects the choice of symbol for the thousands separator used in digit grouping, so the latter is also treated in this article. In mathematics the decimal mark is a type of radix point, in the Middle Ages, before printing, a bar over the units digit was used to separate the integral part of a number from its fractional part, e. g.9995. His Compendious Book on Calculation by Completion and Balancing presented the first systematic solution of linear, a similar notation remains in common use as an underbar to superscript digits, especially for monetary values without a decimal mark, e. g.9995. Later, a separatrix between the units and tenths position became the norm among Arab mathematicians, e. g. 99ˌ95, when this character was typeset, it was convenient to use the existing comma or full stop instead. The separatrix was also used in England as an L-shaped or vertical bar before the popularization of the period, gerbert of Aurillac marked triples of columns with an arc when using his Hindu–Arabic numeral-based abacus in the 10th century. Fibonacci followed this convention when writing numbers such as in his influential work Liber Abaci in the 13th century, in France, the full stop was already in use in printing to make Roman numerals more readable, so the comma was chosen. Many other countries, such as Italy, also chose to use the comma to mark the decimal units position and it has been made standard by the ISO for international blueprints. However, English-speaking countries took the comma to separate sequences of three digits, in some countries, a raised dot or dash may be used for grouping or decimal mark, this is particularly common in handwriting. In the United States, the stop or period was used as the standard decimal mark. g. However, as the mid dot was already in use in the mathematics world to indicate multiplication. In the event, the point was decided on by the Ministry of Technology in 1968, the three most spoken international auxiliary languages, Ido, Esperanto, and Interlingua, all use the comma as the decimal mark. Interlingua has used the comma as its decimal mark since the publication of the Interlingua Grammar in 1951, Esperanto also uses the comma as its official decimal mark, while thousands are separated by non-breaking spaces,12345678,9. Idos Kompleta Gramatiko Detaloza di la Linguo Internaciona Ido officially states that commas are used for the mark while full stops are used to separate thousands, millions. So the number 12,345,678.90123 for instance, the 1931 grammar of Volapük by Arie de Jong uses the comma as its decimal mark, and uses the middle dot as the thousands separator. In 1958, disputes between European and American delegates over the representation of the decimal mark nearly stalled the development of the ALGOL computer programming language. ALGOL ended up allowing different decimal marks, but most computer languages, the 22nd General Conference on Weights and Measures declared in 2003 that the symbol for the decimal marker shall be either the point on the line or the comma on the line. It further reaffirmed that numbers may be divided in groups of three in order to facilitate reading, neither dots nor commas are ever inserted in the spaces between groups
33.
Euler's totient function
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In number theory, Eulers totient function counts the positive integers up to a given integer n that are relatively prime to n. It is written using the Greek letter phi as φ or ϕ and it can be defined more formally as the number of integers k in the range 1 ≤ k ≤ n for which the greatest common divisor gcd is equal to 1. The integers k of this form are referred to as totatives of n. For example, the totatives of n =9 are the six numbers 1,2,4,5,7 and 8. They are all relatively prime to 9, but the three numbers in this range,3,6, and 9 are not, because gcd = gcd =3. As another example, φ =1 since for n =1 the only integer in the range from 1 to n is 1 itself, Eulers totient function is a multiplicative function, meaning that if two numbers m and n are relatively prime, then φ = φφ. This function gives the order of the group of integers modulo n. It also plays a key role in the definition of the RSA encryption system, leonhard Euler introduced the function in 1763. However, he did not at that time choose any specific symbol to denote it. In a 1784 publication, Euler studied the function further, choosing the Greek letter π to denote it, he wrote πD for the multitude of less than D. This definition varies from the current definition for the totient function at D =1 but is otherwise the same, the now-standard notation φ comes from Gausss 1801 treatise Disquisitiones Arithmeticae. Although Gauss didnt use parentheses around the argument and wrote φA, thus, it is often called Eulers phi function or simply the phi function. In 1879, J. J. Sylvester coined the term totient for this function, so it is referred to as Eulers totient function. Jordans totient is a generalization of Eulers, the cototient of n is defined as n − φ. It counts the number of positive integers less than or equal to n that have at least one factor in common with n. There are several formulas for computing φ and it states φ = n ∏ p ∣ n, where the product is over the distinct prime numbers dividing n. The proof of Eulers product formula depends on two important facts and this means that if gcd =1, then φ = φ φ. If p is prime and k ≥1, then φ = p k − p k −1 = p k −1 = p k, proof, since p is a prime number the only possible values of gcd are 1, p, p2
34.
1000
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This article is about the single year 1000, see 1000s, 990s, 10th century, 11th century for events or processes with approximate date 1000. Year 1000 was a year starting on Monday of the Julian calendar. It was also the last year of the 10th century as well as the last year of the 1st millennium of the Dionysian era ending on December 31st, the Muslim world was in its Golden Age. China was in its Song dynasty, Japan was in its classical Heian period, india was divided into a number of lesser empires, such as the Rashtrakuta Dynasty, Pala Empire, Chola dynasty, Yadava dynasty, etc. Sub-Saharan Africa was still in the period, although Arab slave trade was beginning to be an important factor in the formation of the Sahelian kingdoms. The pre-Columbian New World was in a time of transition in many regions. Wari and Tiwanaku cultures receded in power and influence while Chachapoya, mitla, with Mixtec influence, became the more important site of the Zapotec, overshadowing the waning Monte Albán. Cholula flourished in central Mexico, as did Tula, the center of Toltec culture, World population is estimated to have been between c.250 and 310 million. In continental Europe, the Holy Roman Empire established itself as the most powerful state, otto III made a pilgrimage from Rome to Aachen and Gniezno, stopping at Regensburg, Meissen, Magdeburg, and Gniezno. The Congress of Gniezno was part of his pilgrimage, in Rome, he built the basilica of San Bartolomeo allIsola, to host the relics of St. Bartholomew. In France, Robert II, the son of Hugh Capet, was the first of the Capetian kings, the Byzantine Empire under the Macedonian dynasty was engaged in a long and hard war with the First Bulgarian Empire. At the same time, Byzantium was instrumental in the Christianization of the Kievan Rus, in Great Britain, a unified kingdom of England had developed out of the various Anglo-Saxon kingdoms. In Scandinavia, Christianization was in its stages, with the Althingi of the Icelandic Commonwealth embracing Christianity in the year 1000. On September 9, King Olaf Tryggvason was defeated by an alliance of his enemies in the Battle of Svolder, sweyn I established Danish control over part of Norway. The Papacy during this time was in a period of decline, in known as the saeculum obscurum or pornocracy. Hungary was established in 1000 as a Christian state, in the next centuries, the Kingdom of Hungary became the pre-eminent cultural power in the Central European region. On December 25, Stephen I was crowned as the first King of Hungary in Esztergom, sancho III of Navarre became King of Aragon and Navarre. It is believed that in or around this year, Norse explorer Leif Ericson became the first European to land in the Americas, the Château de Goulaine vineyard was founded in France
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1st millennium
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The first millennium was a period of time that began on January 1, AD1, and ended on December 31, AD1000, of the Julian calendar. It was the first period of one years in the Anno Domini or Common Era. In Europe and the Mediterranean, the first millennium was a time of great transition, the 1st century saw the peak of the Roman Empire, followed by its gradual decline during the period of Late Antiquity, the rise of Christianity and the Great Migrations. In Arabia, in the century, a man called Muhammad became the leader. After his death, his companions extended the religion, in East Asia, the first millennium was also a time of great cultural advances, notably the spread of Buddhism to East Asia. In China, the Han dynasty is replaced by the Jin dynasty and later the Tang dynasty until the 10th century sees renewed fragmentation in the Five Dynasties, in Japan, a sharp increase in population followed when farmers use of iron tools increased their productivity and crop yields. In South Asia, the Indian subcontinent was divided among numerous kingdoms throughout the first millennium, in Mesoamerica, the first millennium was a period of enormous growth known as the Classic Era. Teotihuacan grew into a metropolis and its empire dominated Mesoamerica, in South America, pre-Incan, coastal cultures flourished, producing impressive metalwork and some of the finest pottery seen in the ancient world. In North America, the Mississippian culture rose at the end of the millennium in the Mississippi, numerous cities were built, Cahokia, the largest, was based in present-day Illinois, and may have had 30,000 residents at its peak about 1250 AD. The circumference of the 10-story-high Monks Mound at Cahokia was larger than that of the Pyramid of the Sun at Teotihuacan or the Great Pyramid in Egypt
36.
Currency
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A currency in the most specific use of the word refers to money in any form when in actual use or circulation as a medium of exchange, especially circulating banknotes and coins. A more general definition is that a currency is a system of money in common use, under this definition, US dollars, British pounds, Australian dollars, and European euros are examples of currency. These various currencies are recognized stores of value and are traded between nations in exchange markets, which determine the relative values of the different currencies. Currencies in this sense are defined by governments, and each type has limited boundaries of acceptance, other definitions of the term currency are discussed in their respective synonymous articles banknote, coin, and money. The latter definition, pertaining to the systems of nations, is the topic of this article. Currencies can be classified into two systems, fiat money and commodity money, depending on what guarantees the value. Some currencies are legal tender in certain jurisdictions, which means they cannot be refused as payment for debt. Others are simply traded for their economic value, digital currency has arisen with the popularity of computers and the Internet. Currency evolved from two basic innovations, both of which had occurred by 2000 BC, originally money was a form of receipt, representing grain stored in temple granaries in Sumer in ancient Mesopotamia, then Ancient Egypt. In this first stage of currency, metals were used as symbols to represent value stored in the form of commodities and this formed the basis of trade in the Fertile Crescent for over 1500 years. Trade could only reach as far as the credibility of that military and it is not known what was used as a currency for these exchanges, but it is thought that ox-hide shaped ingots of copper, produced in Cyprus, may have functioned as a currency. It is thought that the increase in piracy and raiding associated with the Bronze Age collapse, possibly produced by the Peoples of the Sea, brought the trading system of oxhide ingots to an end. In Africa, many forms of value store have been used, including beads, ingots, ivory, various forms of weapons, livestock, the manilla currency, the manilla rings of West Africa were one of the currencies used from the 15th century onwards to sell slaves. African currency is still notable for its variety, and in many various forms of barter still apply. These factors led to the metal itself being the store of value, first silver, now we have copper coins and other non-precious metals as coins. Metals were mined, weighed, and stamped into coins and this was to assure the individual taking the coin that he was getting a certain known weight of precious metal. Coins could be counterfeited, but they created a new unit of account. Most major economies using coinage had several tiers of coins, using a mix of copper, silver, gold coins were used for large purchases, payment of the military and backing of state activities, they were more often used as measures of account than physical coins
37.
Dollar
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Dollar is the name of more than twenty currencies, including those of the United States, Canada, Australia, Taiwan, Hong Kong, Singapore, New Zealand, Liberia, Jamaica and Namibia. Generally, one dollar is divided into one hundred cents, on 15 January 1520, the Czech Kingdom of Bohemia began minting coins from silver mined locally in Joachimsthal and marked on reverse with the Czech lion. The coins were called joachimsthaler, which became shortened in common usage to thaler or taler, the German name Joachimsthal literally means Joachims valley or Joachims dale. A later Dutch coin also depicting a lion was called the leeuwendaler or leeuwendaalder, the Dutch Republic produced these coins to accommodate its booming international trade. The leeuwendaler circulated throughout the Middle East and was imitated in several German and Italian cities and this coin was also popular in the Dutch East Indies and in the Dutch New Netherland Colony. It was in throughout the Thirteen Colonies during the 17th. The currencies of Romania and Bulgaria are, to this day, the modern American-English pronunciation of dollar is still remarkably close to the 17th century Dutch pronunciation of daler. Some well-worn examples circulating in the Colonies were known as dog dollars, Spanish pesos – having the same weight and shape – came to be known as Spanish dollars. By the time of the American Revolution, Spanish dollars gained significance because they backed paper money authorized by the individual colonies, common in the Thirteen Colonies, Spanish dollars were even legal tender in one colony, Virginia. On April 2,1792, U. S. Secretary of the Treasury Alexander Hamilton reported to Congress the precise amount of found in Spanish dollar coins in common use in the states. As a result, the United States dollar was defined as a unit of silver weighing 371 4/16th grains. It was specified that the money of account of the United States should be expressed in those same dollars or parts thereof, in an act passed in January 1837, the dollars alloy was set at 15%. Subsequent coins would contain the amount of pure silver as previously. On February 21,1853, the quantity of silver in the coins was reduced. However, the dollars constitutional meaning has remained unchanged through the years, silver was mostly removed from U. S. coinage by 1965 and the dollar became a free-floating fiat currency without a commodity backing defined in terms of real gold or silver. The US Mint continues to make silver $1-denomination coins, but these are not intended for general circulation, there are many quotes in the plays of William Shakespeare referring to dollars as money. This might be supported by a reference to the sum of ten dollars in Macbeth. In 1804, a British five-shilling piece, or crown, was sometimes called dollar and it was an overstruck Spanish eight real coin, the original of which was known as a Spanish dollar
38.
Pound (currency)
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The pound is a unit of currency in some nations. The term originated in the Frankish Empire as a result of Charlemagnes currency reform and was taken to Great Britain as the value of a pound of silver. The English word pound is cognate with, among others, German Pfund, Dutch pond, all ultimately derive from a borrowing into Proto-Germanic of the Latin expression lībra pondō, in which the word pondō is the ablative case of the Latin noun pondus. The English word pound first referred to a unit of mass or weight, the currencys symbol is £, a stylised representation of the letter L, standing for livre or lira. Historically, £1 worth of coins were a troy pound in weight. Today, the term may refer to a number of currencies, some of them, those official in former Italian states and in countries formerly belonging to the Ottoman Empire, are called pound in English, while in the local languages their official name is lira. See also Isle of Man pound, Jersey pound, Guernsey pound, egyptian pound Lebanese pound South Sudanese pound Sudanese pound Syrian pound The following currencies are interchangeable at par with the pound sterling. These are issued in the Crown dependencies and certain British Overseas Territories, the Australian pound was also used in the Gilbert and Ellice Islands, Nauru, New Hebrides and Papua and New Guinea. It was replaced in the New Hebrides in 1977 by the New Hebrides franc. S, the Jamaican pound was also used in Cayman Islands and Turks and Caicos Islands until 1968. Libyan pound Malawian pound Maltese pound New Brunswick pound Newfoundland pound New Guinean pound New Zealand pound, the New Zealand pound was also used in the Cook Islands and the Pitcairn Islands. The South African pound was used in Basutoland, Bechuanaland, South West Africa
39.
Y2K
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The Year 2000 problem, also known as the Y2K problem, the Millennium bug, the Y2K bug, or Y2K, was a computer bug related to the formatting and storage of calendar data. Problems were anticipated, and arose, because twentieth-century software often represented the year with only the final two digits—making the year 2000 indistinguishable from 1900. The assumption of a date in such programs caused various errors, such as the incorrect display of dates. It identifies two problems that may exist in computer programs. First, the practice of representing the year with two digits became problematic with logical error arising upon rollover from x99 to x00. This had caused some date-related processing to operate incorrectly for dates and times on and after 1 January 2000, without corrective action, long-working systems would break down when the. Ascending numbering assumption suddenly became invalid, years divisible by 100 are not leap years, except for years that are divisible by 400. Thus the year 2000 was a leap year, companies and organisations worldwide checked, fixed, and upgraded their computer systems to address the anticipated problem. Very few computer failures were reported when the clocks rolled over into 2000 and it is not known how many problems went unrecorded. Y2K is a numeronym and was the abbreviation for the year 2000 software problem. The abbreviation combines the letter Y for year, and k for the SI unit prefix kilo meaning 1000, hence, 2K signifies 2000. It was also named the Millennium Bug because it was associated with the popular roll-over of the millennium, the Year 2000 problem was the subject of the early book, Computers in Crisis by Jerome and Marilyn Murray. The first recorded mention of the Year 2000 Problem on a Usenet newsgroup occurred on Friday,18 January 1985, the acronym Y2K has been attributed to David Eddy, a Massachusetts programmer, in an e-mail sent on 12 June 1995. He later said, People were calling it CDC, FADL, Y2K just came off my fingertips. It was therefore important for programmers to reduce usage. As space on disc and tape was also expensive, this also saved money by reducing the size of stored data files, many computer programs stored years with only two decimal digits, for example,1980 was stored as 80. Some such programs could not distinguish between the year 2000 and the year 1900, other programs tried to represent the year 2000 as 19100. This could cause a failure and cause date comparisons to produce incorrect results
40.
Gambling
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Gambling is the wagering of money or something of value on an event with an uncertain outcome with the primary intent of winning money and/or material goods. Gambling thus requires three elements be present, consideration, chance and prize, the term gaming in this context typically refers to instances in which the activity has been specifically permitted by law. However, this distinction is not universally observed in the English-speaking world, for instance, in the United Kingdom, the regulator of gambling activities is called the Gambling Commission. Gambling is also an international commercial activity, with the legal gambling market totaling an estimated $335 billion in 2009. In other forms, gambling can be conducted with materials which have a value, many popular games played in modern casinos originate from Europe and China. Games such as craps, baccarat, roulette, and blackjack originate from different areas of Europe, a version of keno, an ancient Chinese lottery game, is played in casinos around the world. In addition, pai gow poker, a hybrid between pai gow and poker is also played, many jurisdictions, local as well as national, either ban gambling or heavily control it by licensing the vendors. Such regulation generally leads to gambling tourism and illegal gambling in the areas where it is not allowed, there is generally legislation requiring that the odds in gaming devices are statistically random, to prevent manufacturers from making some high-payoff results impossible. Since these high-payoffs have very low probability, a bias can quite easily be missed unless the odds are checked carefully. Most jurisdictions that allow gambling require participants to be above a certain age, in some jurisdictions, the gambling age differs depending on the type of gambling. For example, in many American states one must be over 21 to enter a casino, E. g. Nonetheless, both insurance and gambling contracts are typically considered aleatory contracts under most legal systems, though they are subject to different types of regulation. Under common law, particularly English Law, a contract may not give a casino bona fide purchaser status. For case law on recovery of gambling losses where the loser had stolen the funds see Rights of owner of money as against one who won it in gambling transaction from thief. This was a plot point in a Perry Mason novel, The Case of the Singing Skirt. Religious perspectives on gambling have been mixed, ancient Hindu poems like the Gamblers Lament and the Mahabharata testify to the popularity of gambling among ancient Indians. However, the text Arthashastra recommends taxation and control of gambling, ancient Jewish authorities frowned on gambling, even disqualifying professional gamblers from testifying in court. For these social and religious reasons, most legal jurisdictions limit gambling, in at least one case, the same bishop opposing a casino has sold land to be used for its construction. Although different interpretations of law exist in the Muslim world
41.
A picture is worth a thousand words
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A picture is worth a thousand words is an English idiom. It refers to the notion that an idea can be conveyed with just a single still image or that an image of a subject conveys its meaning or essence more effectively than a description does. Appears in a 1911 newspaper article quoting newspaper editor Tess Flanders discussing journalism, a similar phrase, One Look Is Worth A Thousand Words, appears in a 1913 newspaper advertisement for the Piqua Auto Supply House of Piqua, Ohio. The December 8,1921 issue carries an ad entitled, One Look is Worth A Thousand Words, another ad by Barnard appears in the March 10,1927, issue with the phrase One Picture Worth Ten Thousand Words, where it is labeled a Chinese proverb. The Home Book of Proverbs, Maxims, and Familiar Phrases quotes Barnard as saying he called it a Chinese proverb, nonetheless, the proverb soon after became popularly attributed to Confucius. The actual Chinese expression Hearing something a hundred times isnt better than seeing it once is sometimes introduced as an equivalent and this was published as early as 1966 discussing persuasion and selling in a book on engineering design. In March 1911, in the Syracuse Advertising Mens Club, Arthur Brisbane wrote, despite this modern origin of the popular phrase, the sentiment has been expressed by earlier writers. For example, the Russian writer Ivan Turgenev wrote, The drawing shows me at one glance what might be spread over ten pages in a book, the quote is sometimes attributed to Napoleon Bonaparte, who said A good sketch is better than a long speech. While this is translated today as A picture is worth a thousand words. Show me your tables, and I won’t usually need your flowcharts, the phrase has also been spoofed by computer scientist John McCarthy, to make the opposite point, As the Chinese say,1001 words is worth more than a picture. Cliché The Commissar Vanishes The Dictionary of Clichés by James Rogers, the Commissar Vanishes, The Falsification of Photographs and Art in Stalins Russia. New York, NY, Metropolitan Books,1 edition
42.
Thousand origami cranes
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Thousand Origami Cranes is a group of one thousand origami paper cranes held together by strings. An ancient Japanese legend promises that anyone who folds a thousand cranes will be granted a wish by the gods. Some stories believe you are granted happiness and eternal good luck, instead of just one wish and this makes them popular gifts for special friends and family. The crane in Japan is one of the mystical or holy creatures and is said to live for a thousand years, That is why 1000 cranes are made, one for each year. In some stories it is believed that the 1000 cranes must be completed one year. Cranes that are made by person and given away to another arent included. A thousand paper cranes are given as a wedding gift by the father. They can also be given to a new baby for long life, hanging them in ones home is thought to be a powerfully lucky and benevolent charm. Several temples, including some in Tokyo and Hiroshima, have eternal flames for world peace, at these temples, school groups or individuals often donate senbazuru to add to the prayer for peace. The cranes are left exposed to the elements, slowly dissolving and becoming tattered as the wish is released, in this way they are related to the prayer flags of India and Tibet. The Japanese space agency JAXA used folding 1000 cranes as one of the tests for its potential astronauts. There is a statue of Sadako holding a crane in Hiroshima Peace Park, and every year on Obon day, people leave cranes at the statue in memory of the departed spirits of their ancestors. Sets of origami paper are sold widely in Japan, with senbazuru sets including 1000 sheets of paper, string, commonly the cranes are assembled as 25 strings of 40 cranes each. The size of the paper does matter when assembling a thousand paper cranes. The most popular size for senbazuru is 7.5 by 7.5 centimetres, some people cut their own squares of paper from anything available, such as magazines, newspapers, notebooks, and printer paper. Origami paper used for senbazuru is usually of a solid color, larger size origami paper, usually 6x6 inches, often has traditional Japanese or flower designs, reminiscent of kimono patterns. Childrens Peace Monument Kunihiko Kasahara Sadako and the Thousand Paper Cranes Sadako Sasaki Orizuru
43.
Thousand Oaks, California
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Thousand Oaks is a city in southeastern Ventura County, California, United States. It is in the part of the Greater Los Angeles Area. It was named after the oak trees that grow in the area. The city forms the core of the Conejo Valley, which includes Thousand Oaks proper, Newbury Park, Westlake Village, Agoura Hills. The Los Angeles County–Ventura County line crosses at the eastern border with Westlake Village. The population was estimated to be 129,339 in 2015, Thousand Oaks and Newbury Park were part of a master-planned city, created by the Janss Investment Company in the mid-1950s. It included about 1,000 custom home lots,2,000 single-family residences, a shopping center. The median home price is around $669,500, Thousand Oaks was ranked the fourth-safest among cities with a population greater than 100,000 in the United States by the FBIs 2013 Uniform Crime Reports. The area was occupied by the Chumash people, and 2000-year-old cave drawings may still be seen at the Chumash Indian Museum,3290 Lang Ranch Parkway. The Chumash village was known as Sapwi, which means House of the Deer, the areas recorded history dates to 1542 when Spanish explorer Juan Rodriguez Cabrillo landed at Point Mugu and claimed the land for Spain. It eventually became part of the 48,671 acres Rancho El Conejo land grant by the Spanish government and it served as grazing land for vaqueros for the next fifty years. In the late 19th century it was on the route between Los Angeles and Santa Barbara. The Stagecoach Inn was built in 1876, and is now a California Historical Landmark, the Janss family, developers of Southern California subdivisions, purchased 10,000 acres in the early 20th century. They eventually created plans for a community and the name remains prominently featured in the city. Jungleland USA was one of Southern Californias first theme parks, wild animal shows entertained thousands in the 1940s and 1950s. Many television and movie productions used the parks trained animals and were filmed there, including Birth of a Nation, Tarzan, jungleland closed in May 1968, in part due to competition from other amusement parks such as Knotts Berry Farm and Disneyland. The Thousand Oaks Civic Arts Center today stands on the site of the park, the City of Thousand Oaks was incorporated on October 7,1964, the first incorporated city in the Conejo Valley. Some sources mistakenly state that Thousand Oaks was incorporated on September 29,1964 and it is known for being a planned community, as the city is one of few that have actually stayed with the master plan
44.
Thousand Island dressing
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It also typically contains finely chopped ingredients, which can include pickles, onions, bell peppers, green olives, hard-boiled egg, parsley, pimento, chives, garlic, or chopped nuts. Within that region, one version of the dressings origins says that a fishing guides wife. Often in this version, actress May Irwin requested the recipe after enjoying it, Irwin in turn gave it to another Thousand Islands summer resident, George Boldt, who built Boldt Castle between 1900 and 1904. Boldt, as proprietor of the Waldorf-Astoria Hotel, instructed the hotels maître dhôtel, Oscar Tschirky, a 1959 National Geographic article states, Thousand Island Dressing was reportedly developed by Boldts chef. All the claims appeared to be based upon oral traditions without supporting written records, some food writers advance the claim that the dressing was invented by chef Theo Rooms of the Blackstone Hotel in Chicago during the same time period. In the 1950s, Thousand Island dressing became a standard condiment, used on sandwiches and it is widely used in fast-food restaurants and diners in the United States, where it is often referred to as Special Sauce or Secret Sauce. An example of this is In-N-Out Burgers Spread, served on burgers and several Secret Menu items, despite its name, Thousand Island dressing is often used in a Reuben sandwich in lieu of Russian dressing. Fry sauce Russian dressing Marie Rose sauce Salsa golf Thousand Islands, Thousand Islands Dressing early printed citations collected by Barry Popik
45.
Thousand Foot Krutch
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Thousand Foot Krutch is a Canadian Christian rock band formed in 1995. They have also released one album and three remix albums. Singer Trevor McNevan and drummer Steve Augustine are also members of their own project band called FM Static. The band has sold a million albums as of February 2014, Trevor McNevan founded the band in Peterborough, Ontario, a city northeast of Toronto, where he went to high school. Joel Bruyere, born in Brantford, Ontario, was McNevans childhood friend who had moved away, drummer Steve Augustine is from Hamilton, Ontario. McNevans first band was Oddball, which featured Dave Smith on guitar, Tim Baxter on bass and McNevans good friend, Oddball recorded only one album, Shutterbug, which was released in 1995. McNevan is the member of TFK, formed in 1997 in Peterborough. McNevan came up with TFKs name symbolizing the point in our lives that we realize we cant make it on our own strength and he has written and released seven albums with Thousand Foot Krutch to date and another four with his side project FM Static. TFK has worked with Aaron Sprinkle, Gavin Brown, Arnold Lanni, Shutterbug was released by Trevor McNevan in 1995 under the band name Oddball. McNevan had friends Dave Smith, Tim Baxter and Neil Sanderson, there were 27 songs on the album, the first half rock, the second half hip-hop. McNevan recorded it at Barry Haggartys studio in his town of Peterborough, Ontario. He worked at McDonalds and other jobs to pay for the studio time, the song Lift It, first appeared here and was later re-recorded for Thousand Foot Krutchs first release Thats What People Do and appeared again on Set It Off. Thats What People Do was written the year McNevan started TFK in 1997 and it was released independently in 1998 and is out of print. TFK climbed the ladder of local notoriety throughout Ontario and abroad, reaching the ears of Ontario commercial radio, CKWF101.5 FM in their home town of Peterborough added Rhyme Animal, the bands first single from their independent recording, to their rotation. It clicked with listeners and within two months ended up being one of the five most requested songs of the year, in 1999, TFK was chosen by 7 Ball Magazine as one of the top 25 bands in North America. They were also awarded Best Indie Recording and McNevan awarded Vocalist of the Year by the readers of The Wire Magazine and they were then awarded Band of the Year at the 2000 Wire Awards. They were also voted as the No.1 band of the millennium on 100.3 FM in Barrie, Set It Off was released on November 14,2000. It was the groups first indie label release, the band toured it extensively across North America and ended up garnering much label attention by selling 85,000 copies of the indie release out of their van
46.
Alternative rock
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Alternative rock is a genre of rock music that emerged from the independent music underground of the 1980s and became widely popular in the 1990s and 2000s. In this instance, the word refers to the genres distinction from mainstream rock music. The terms original meaning was broader, referring to a generation of musicians unified by their debt to either the musical style or simply the independent. Ethos of punk rock, which in the late 1970s laid the groundwork for alternative music, Alternative rock is a broad umbrella term consisting of music that differs greatly in terms of its sound, its social context, and its regional roots. Most of these subgenres had achieved minor mainstream notice and a few bands representing them, such as Hüsker Dü, with the breakthrough of Nirvana and the popularity of the grunge and Britpop movements in the 1990s, alternative rock entered the musical mainstream and many alternative bands became successful. By the end of the decade, alternative rocks mainstream prominence declined due to a number of events that caused grunge and Britpop to fade, emo attracted attention in the larger alternative rock world, and the term was applied to a variety of artists, including multi-platinum acts. Post-punk revival artists such as Modest Mouse and The Killers had commercial success in the early, before the term alternative rock came into common usage around 1990, the sort of music to which it refers was known by a variety of terms. In 1979, Terry Tolkin used the term Alternative Music to describe the groups he was writing about, in 1979 Dallas radio station KZEW had a late night new wave show entitled Rock and Roll Alternative. College rock was used in the United States to describe the music during the 1980s due to its links to the radio circuit. In the United Kingdom, dozens of small do it yourself record labels emerged as a result of the punk subculture, according to the founder of one of these labels, Cherry Red, NME and Sounds magazines published charts based on small record stores called Alternative Charts. The first national chart based on distribution called the Indie Chart was published in January 1980, at the time, the term indie was used literally to describe independently distributed records. By 1985, indie had come to mean a particular genre, or group of subgenres, at first the term referred to intentionally non–mainstream rock acts that were not influenced by heavy metal ballads, rarefied new wave and high-energy dance anthems. The use of alternative gained further exposure due to the success of Lollapalooza, for which festival founder, in the late 1990s, the definition again became more specific. Defining music as alternative is often difficult because of two conflicting applications of the word, the name alternative rock essentially serves as an umbrella term for underground music that has emerged in the wake of punk rock since the mid-1980s. Alternative bands during the 1980s generally played in clubs, recorded for indie labels. Sounds range from the gloomy soundscapes of gothic rock to the guitars of indie pop to the dirty guitars of grunge to the 1960s/1970s revivalism of Britpop. This approach to lyrics developed as a reflection of the social and economic strains in the United States and United Kingdom of the 1980s, by 1984, a majority of groups signed to independent record labels mined from a variety of rock and particularly 1960s rock influences. This represented a break from the futuristic, hyper-rational post-punk years
47.
Techno
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Techno is a form of electronic dance music that emerged in Detroit, Michigan, in the United States during the mid-to-late 1980s. The first recorded use of the word techno in reference to a genre of music was in 1988. Many styles of techno now exist, but Detroit techno is seen as the foundation upon which a number of subgenres have been built. Added to this is the influence of futuristic and fictional themes relevant to life in American late capitalist society, pioneering producer Juan Atkins cites Tofflers phrase techno rebels as inspiring him to use the word techno to describe the musical style he helped to create. This unique blend of influences aligns techno with the referred to as afrofuturism. To producers such as Derrick May, the transference of spirit from the body to the machine is often a central preoccupation, in this manner, techno dance music defeats what Adorno saw as the alienating effect of mechanisation on the modern consciousness. Stylistically, techno is generally repetitive instrumental music, oftentimes produced for use in a continuous DJ set, the tempo tends to vary between approximately 120 to 150 beats per minute, depending on the style of techno. The creative use of production technology, such as drum machines, synthesizers. Many producers use retro electronic musical devices to create what they consider to be an authentic techno sound, drum machines from the 1980s such as Rolands TR-808 and TR-909 are highly prized, and software emulations of such retro technology are popular among techno producers. The Electrifying Mojo was the first radio DJ to play music by the Detroit techno producers Juan Atkins, Derrick May, Mojo refused to follow pre-established radio formats or playlists, and he promoted social and cultural awareness of the African American community. In exploring technos origins writer Kodwo Eshun maintains that Kraftwerk are to Techno what Muddy Waters is to the Rolling Stones, the authentic, the origin, the real. Juan Atkins has acknowledged that he had an enthusiasm for Kraftwerk and Giorgio Moroder, particularly Moroders work with Donna Summer. Atkins also mentions that around 1980 I had a tape of nothing but Kraftwerk, Telex, Devo, Giorgio Moroder and Gary Numan, and Id ride around in my car playing it. Regarding his initial impression of Kraftwerk, Atkins notes that they were clean, Derrick May identified the influence of Kraftwerk and other European synthesizer music in commenting that it was just classy and clean, and to us it was beautiful, like outer space. Living around Detroit, there was so little beauty, everything is an ugly mess in Detroit, and so we were attracted to this music. May has commented that he considered his music a direct continuation of the European synthesizer tradition and he also identified Japanese synthpop act Yellow Magic Orchestra, particularly member Ryuichi Sakamoto, and British band Ultravox, as influences, along with Kraftwerk. In 1980 or 1981 they met with Mojo and proposed that they provide mixes for his show, which they did end up doing the following year. These young promoters developed and nurtured the local music scene by both catering to the tastes of the local audience of young people and by marketing parties with new DJs
48.
Moby
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Richard Melville Hall, better known by his stage name Moby, is an American DJ, singer, songwriter, musician, photographer and animal rights activist. He is well known for his music, veganism. Moby has sold over 20 million records worldwide, allMusic considers him one of the most important dance music figures of the early 1990s, helping bring the music to a mainstream audience both in the UK and in America. Moby gained attention in the early 1990s with his dance music work. With his fifth album, the electronica and house music-influenced Play. His next major release, 2005s mostly upbeat Hotel was a departure, incorporating more alternative rock elements than previous albums. It sold around 2 million copies worldwide, Moby released Innocents on October 1,2013 to positive reviews. Following the release of Innocents, Moby released the ambient album, Long Ambients 1, the album was given away for free on his website. Mobys most recent album These Systems Are Failing was released on October 14,2016, the album has received mostly positive reviews. He was raised by his mother in Darien, Connecticut and he has also released music under the names Voodoo Child and Schaumgummi. During the 1980s, Hall played guitar for the punk band Vatican Commandos. Later in the decade, he was a guitarist for the rock group Ultra Vivid Scene. It left me very intrigued and impressed in a strange way, Moby released his first singles for Instinct under several different names, such as Barracuda, Brainstorm, and UHF. His first single was a commercial failure—a rap record with vocalist Jimmy Mack, titled Times Up, featuring several remixes, very few copies were ever sold. His first single under the pseudonym Moby was Mobility, but it was his remix of Mobilitys b-side, Go and he released his eponymous debut in 1992. Some of his singles in 1992 and 1993 were Next Is the E, Thousand. In 1991 and 1992 he remixed The B-52s, The Prodigy, Orbital, Bob Taggett - Mind Metal, Erasure, Michael Jackson and he also provided a rap for a Recoil track called Curse. In 1993, Moby signed with Mute Records and released an EP titled Move and this became his second appearance on Top of the Pops
49.
A Thousand Suns
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For the 1991 Russell Morris album of the same name, see A Thousand Suns A Thousand Suns is the fourth studio album by American rock band Linkin Park. It was released on September 8,2010, by Warner Bros, the album was written by the band and was produced by Linkin Park vocalist Mike Shinoda and Rick Rubin, who worked together to produce the bands previous studio album Minutes to Midnight. Recording sessions for A Thousand Suns took place at NRG Recording Studios in North Hollywood, a Thousand Suns is a multi-concept album dealing with human fears such as nuclear warfare. The band has said the album is a departure from their previous work, they experimented on different. Shinoda told MTV the album references numerous social issues and blends human ideas with technology. The title is a reference to Hindu Sanskrit scripture, a line of which was first popularized in 1945 by J. Robert Oppenheimer and it also appears in a line from the first single of the album, The Catalyst. The Catalyst was sent to radio and released to music retailers on August 2,2010. The Catalyst peaked at the Billboard Alternative Songs and Rock Songs charts, three more singles were released to promote the album, Waiting for the End, Burning in the Skies and Iridescent. The Catalyst and Waiting for the End were certified gold by the Recording Industry Association of America, Linkin Park promoted the album through the A Thousand Suns World Tour from October 2010 to September 2011. Upon release, the album polarized critics and fans, the bands fanbase divided over their new sound, splitting them into love-it versus hate-it groups according to one reviewer. Despite this, the album has been a success, debuting at number one on over ten charts. It was certified gold by the RIAA in February 2011, by June 2014, it had sold over 960,000 copies in the United States according to Nielsen SoundScan. Recording for the album began in 2008, less than a year after the release of Minutes to Midnight, as with Minutes to Midnight, Shinoda and Rick Rubin produced the album. Primary recording sessions for A Thousand Suns took place at NRG Recording Studios in North Hollywood, Los Angeles and it was an inspiring idea, and it was something we could relate a lot of the things we like to write about to. In May 2009, Mike Shinoda revealed info on the album in a Billboard magazine story, saying, id say weve got about half the music done, though I shouldnt say halfway because who knows how long the next batch of songs will take. But all the materials just kind of coming together, and every week we meet up and assess the situation and for the rest of the week we just go and work on whatever we find exciting. He also explained the experimentation that the band would be working with, saying and its not going to be Minutes to Midnight. And if we do it right, itll have a cutting edge sound that defines itself as an individual separate from anything else thats out there
50.
Linkin Park
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Linkin Park is an American rock band from Agoura Hills, California. Formed in 1996, the rose to international fame with their debut album Hybrid Theory. Their following studio album Meteora continued the success, topping the Billboard 200 album chart in 2003. In 2003, MTV2 named Linkin Park the sixth-greatest band of the video era. Billboard ranked Linkin Park No.19 on the Best Artists of the Decade chart, in 2012, the band was voted as the greatest artist of the 2000s in a Bracket Madness poll on VH1. In 2014, the band was declared as the Biggest Rock Band in the World Right Now by Kerrang. Having adapted nu metal and rap metal to a radio-friendly yet densely layered style in Hybrid Theory and Meteora, the album topped the Billboard charts and had the third-best debut week of any album that year. The band continued to explore a wider variation of musical types in their album, A Thousand Suns, layering their music with more electronic sounds. Their fifth album, Living Things, combines elements from all of their previous records. Their sixth album, The Hunting Party, returned to a rock sound. Their upcoming album One More Light is expected to be released May 19,2017, the band has collaborated with several other artists, most notably with rapper Jay Z in their mashup EP Collision Course, and many others on the remix albums Reanimation and Recharged. Linkin Park has sold over 70 million albums worldwide and has won two Grammy Awards, Linkin Park was founded by three high school friends, Mike Shinoda, Rob Bourdon, and Brad Delson. The three attended Agoura High School in Agoura Hills, California, a suburb of Los Angeles. After graduating from school, the three began to take their musical interests more seriously, recruiting Joe Hahn, Dave Phoenix Farrell. Though limited in resources, the began recording and producing songs within Shinodas makeshift bedroom studio in 1996, resulting in a four-track demo tape. Tensions and frustration within the band grew however after they failed to land a record deal, the lack of success and stalemate in progress prompted Wakefield, at that time the bands vocalist, to leave the band in search of other projects. Farrell also left to tour with Tasty Snax, a Christian punk, Bennington, formerly of a post-grunge band by the name of Grey Daze, became a standout among applicants because of the dynamic in his singing style. The band then agreed on changing its name from Xero to Hybrid Theory, in 1999 the band released a self-titled extended play, which they circulated across internet chat-rooms and forums with the help of an online street team
51.
A Thousand Years (Christina Perri song)
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A Thousand Years is a song by American singer-songwriter Christina Perri and David Hodges. It is taken from the album The Twilight Saga, Breaking Dawn — Part 1, the song serves as the second single from the album. The song was released as a download on October 18,2011 worldwide. Perri re-recorded the song with vocals from Steve Kazee for the The Twilight Saga, Breaking Dawn — Part 2, Original Motion Picture Soundtrack titled A Thousand Years, Pt.2. An official lyric video of the song was premiered on October 17,2011 via Perris official Facebook, on October 26,2011, she released an official video for the song on her YouTube channel. The video begins with Perri holding a candle and it features a few clips from the movie interspersed between scenes with Perri singing in a room with a floor full of candles. The video may include the voices from Kristen Stewart and Robert Pattinson saying they love each other while in a wedding and she ends the video singing into a sunset. On the week of October 23,2011, the song debuted at No.63 on the US Billboard Hot 100 chart and it has reached number 31 on the Billboard Hot 100, giving Perri her second top 40 hit. By July 2013, the song has sold over 3 million digital downloads in the US, as of June 2014, the song has sold 3,657,000 copies in the US. In the United Kingdom, the reached number 32 on its original release in 2011. The following year, after the release of The Twilight Saga, Breaking Dawn – Part 2, in 2013, after it was performed on the The X Factor, it reached a new peak of 11. Video on her channel on YouTube
52.
Christina Perri
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Christina Judith Perri is an American singer and songwriter from Bucks County, Pennsylvania. After her debut single Jar of Hearts was featured on the Fox television series So You Think You Can Dance in 2010, Perri released her extended play. Soon after, she signed with Atlantic Records and released her studio album. Perri also gained recognition for writing and recording A Thousand Years, the theme for the film The Twilight Saga, Breaking Dawn – Part 2. The song went on to sell over 4 million copies in the United States and she later released her second extended play, A Very Merry Perri Christmas, followed by her second studio album, Head or Heart. Perri was born in Bensalem, Pennsylvania to Mary and Dante Perri and she has an older brother, Nick Perri, who formerly played guitar with Shinedown, Silvertide, Perry Farrell and Matt Sorum and cousin Dominic Perri Her father was from Italy. She graduated from Archbishop Ryan High School in 2004 and she taught herself how to play guitar as a 16-year-old by watching a videotape of Shannon Hoon from the group Blind Melon performing on VH1. She attended college as a major for a year before dropping out to pursue a music career. She frequently sang and acted in theatre as a child. Perri claims to have learned to play piano and guitar because she missed hearing music being played in the house when she moved away, according to Perri, whenever she played the guitar or piano, she would sing and all of a sudden these songs would appear. Perri moved to Los Angeles on her 21st birthday, according to Perri, she felt terrified of being over 3000 miles away from her family, saying that she cried eyes out every day. Later that year she married and began to produce videos for a living. She divorced 18 months later and moved in to an apartment on her own to focus entirely on working on music. She moved back to Philadelphia by the end of 2009, it was during this time that she wrote Jar of Hearts and she later moved back to Los Angeles, waitressing at the Melrose Cafe during the day and recording at night. Perris song Jar of Hearts was featured on So You Think You Can Dance during the show of June 30,2010 in a performance by Billy Bell, Perris friend Keltie Knight passed the song to show choreographer Stacey Tookey, as Perri was unsigned at the time. Perri and Colleen watched the performance in the audience, following its exposure on the show, Jar of Hearts sold 48,000 digital copies in its first week, debuting on the Billboard Hot 100 at No.63 and reaching No.28 on Billboards Hot Digital Songs. Within a month, it had more than 100,000 copies. The song peaked at number 17 on the Hot 100, following the success of Jar of Hearts, Perri signed a deal with Atlantic Records on July 21,2010
53.
A Thousand Miles
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A Thousand Miles is the debut single written and recorded by American pop singer Vanessa Carlton. Produced by Curtis Schweitzer and Ron Fair, the song was released as the single for Carltons album Be Not Nobody. Her signature song, it became Carltons breakthrough hit and one of the most popular songs of the year, to date, it remains Carltons biggest hit in the United States, and her only single to reach the top ten of the Billboard Hot 100. Due to its success, it was featured on the 2002 US compilation album Now Thats What I Call Music. It has been covered by artists including Icarus the Owl, Victoria Justice, David Archuleta, Terry Crews and the Glee Cast. A Thousand Miles is a pop song supported by a string orchestral arrangement. Carlton said that she wrote the song about her grandfather, who had died earlier and she has also called the song a combination of reality and fantasy. Its about a love that so consumes you that you do anything for it, Thats how I felt at that time. A Thousand Miles is written in the key of B major, Carlton wrote the songs piano riff in the summer of 1998 at her parents house in Philadelphia, her mother, who had been listening to her, said, Vanessa, thats a hit song. Carlton was unable to finish the song because of a case of writers block, while looking for a record label that would sign her, Carlton played the beginning of the song for a record producer, who said, You have to finish that. She returned to her parents home and finished it in a one evening, naming it Interlude. Some years later, Carlton recorded a tape and sent it to various producers. Some expressed interest, but Carlton did not agree with their suggestions for alternative titles for the song. One of the tapes found its way to Ron Fair, head of A&M Records, who recalled that It was extraordinary and it didnt press the emotional buttons the way I envisioned it. Carlton met with Fair for a session to alter the arrangement of the song, so the heartbeat came in a different way. During the session, more time signatures and transitions were inserted into the song, additionally, the instrumental opening was shortened and an orchestra section was added by Fair, the lyrics, however, remained the same. He explained, It has a lot of starts and stops to it, which makes it hard to achieve a flow, the song is like a mini musical of its own. A Thousand Miles took fourteen sessions to record, and was the first song recorded for Be Not Nobody
54.
Vanessa Carlton
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Vanessa Lee Carlton is an American singer-songwriter. Upon completion of her education at the School of American Ballet, Carlton chose to pursue singing instead, performing in New York City bars, three months after recording a demo with producer Peter Zizzo, she signed with A&M Records. She began recording her album, which was unsuccessful until Ron Fair took over. Her debut single, A Thousand Miles, reached the top five on the Billboard Hot 100 in 2002 and her debut album, Be Not Nobody, followed and received a platinum certification in the United States. Her subsequent albums, Harmonium and Heroes & Thieves, failed to match the success of the first. She produced an album, Rabbits on the Run, independently before seeking a record label to release it. Carlton released a holiday EP titled Hear the Bells in November 2012, Carlton was born in Milford, Pennsylvania, the first of three children of Edmund Ed Carlton, a pilot, and Heidi Lee, a pianist and school music teacher. Her two younger siblings are a sister, Gwen, and a brother, Edmund, Carlton is of half Russian Jewish and half Scandinavian ancestry. Her interest in music began at an early age, at the age of 2, she visited Disneyland Park and played Its a Small World on the piano when she came home. Her mother then began to tutor her and she was introduced to classical music from a young age. By the age of 9, she had become passionate about ballet, in 1994, when Carlton was 14 years old, she enrolled at the School of American Ballet. Upon graduation, she put on performances at nightclubs in the community, beginning to feel more comfortable. Carlton was signed to A&M Records in 2001, Carlton first met songwriter/producer Peter Zizzo at a singer-songwriter circle. A few months later, Zizzo invited Carlton to his studio to record a demo, three months after recording the demo, Carlton was signed by Jimmy Iovine and began to record the album, Rinse. It was never released, but a few tracks were reworked for Be Not Nobody, one song, Carnival, was re-recorded as Dark Carnival for the video game SpyHunter 2. Other tracks included in Rinse are Interlude, Rinse, Ordinary Days, Twilight, Pretty Baby, All I Ask, of these, only the first five are included in her first album, Be Not Nobody. Other unreleased tracks from her early demo tapes include Faces, Meggie Sue, Little Mary, Burden, Wonder, Devil Dance, with her previous unsuccessful recording efforts, Carlton felt there was a lack of direction at her label. However, A&M president Ron Fair upon hearing her demo to A Thousand Miles, Fair would produce the rest of the album
55.
The Hives
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The Hives are a Swedish rock band that rose to prominence in the early 2000s during the garage rock revival. Their mainstream success came with the release of the album Veni Vidi Vicious, the band have been acclaimed by music critics as one of the best live rock bands in current music. The Hives have released five albums, Barely Legal, Veni Vidi Vicious, Tyrannosaurus Hives, The Black and White Album. They have one album, Your New Favourite Band and they have issued a live DVD. The band claims it was formed in 1993 under the guidance of Randy Fitzsimmons, Fitzsimmons suggested that they form a garage rock band. He gave each member a letter asking them to start the band. Fitzsimmons allegedly acts as a songwriter and manager for the band, the band recorded a demo titled Sounds Like Sushi in 1994. The following year they were signed to Burning Heart, a Swedish skate punk record label, the following year they released their debut EP Oh Lord. Almqvist decided to promote the band to Burning Heart, in 1997 they released an album called Barely Legal, and began touring. The following year released their second EP A. K. A. They released their studio album Veni Vidi Vicious in April 2000 through Burning Heart Records. The band themselves described the album as being like a glove with brass knuckles. The album yielded the singles Hate to Say I Told You So, Main Offender, Die, All Right. and Supply and Demand. After seeing the video for Hate to Say I Told You So on German TV, Poptones released the best of compilation Your New Favourite Band in 2001, which proved to be their breakthrough record, reaching No.7 in the UK album charts. Following the success of the album, the band re-released singles Hate to Say I Told You So and Main Offender which reach numbers No.23, the band also re-released Veni Vidi Vicious in the US. The Hives - Introduce the Metric System in Time was included on the punk rock sampler album Punk-O-Rama Volume 5 from Epitaph Records. It was during the promotion of Veni Vidi Vicious and Your New Favourite Band that the Hives signed a deal with Universal Music. This led to a dispute between the Hives and Burning Heart, who claimed that the Hives were still contracted to them for one more album
56.
1000hp
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1000hp is the lead single and title track from Godsmacks sixth studio album of the same name. 1000hp was released on June 9,2014, and was available for digital download on Amazon. The single reached number one on the Billboard Hot Mainstream Rock Tracks, when interviewed by Full Metal Jackie, Erna offered additional details as how the single came to be, stating, We had been working on stuff that we had on our own and brought in. We haven’t wrote anything yet, Im just going to write a real quick before TC gets back from dinner. Tony, kidding around, said, You should make it a real fast riff because hell be right back, so I started playing really fast and then all of a sudden, I was like, Hold on. I started hearing the different movements in the chords and it just started to feel like it was coming together, then all of a sudden, within 90 minutes the whole song kind of wrote itself. Digital single On August 12, the video for 1000hp premiered on Shazam. One day later, it premiered on Godsmacks official Vevo channel, on August 4, Godsmack took the stage at the iHeartRadio Theater in New York City as part of the iHeartRadio Live Series for an intimate live performance. The show, which was streamed online, saw the band perform 1000hp live for the first time, florino concluded his review by saying, Its the kind of tune you could hear at sports events and during high-octane action movie set pieces for years to come. Its exactly how real rock should sound in 2014, and its one of the best singles of the year, however, she went on to say that the song holds its own in the bands library of rock tunes. Upon its release, 1000hp entered both the Billboard Mainstream Rock and Hot Rock Songs charts, peaking at one and twenty-two. 1000hp also debuted at one on the U. S. iTunes Rock Chart
57.
Godsmack
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Godsmack is an American rock band from Lawrence, Massachusetts, formed in 1995. The band is composed of founder, frontman and songwriter Sully Erna, guitarist Tony Rombola, bassist Robbie Merrill, since its formation, Godsmack which has resulted in six studio albums, one EP, four DVDs, one compilation album, and one live album. The band has had three consecutive albums on the Billboard 200. The band also has 20 top ten rock radio hits, including 15 songs in the top five, a record number of top ten singles by a rock artist. Since its inception, Godsmack has toured on Ozzfest on more than one occasion, Godsmack has sold over 20 million records in just over a decade. In honor of the success and the release of their sixth studio album, 1000hp. In February 1995, Sully Erna decided to start a new band as the singer after playing the drums for more than 23 years. His new band, The Scam, formed with Erna on vocals, Robbie Merrill on bass, local guitarist and friend Lee Richards on guitar, the Scam quickly changed its name to Godsmack, after recording one demo. The newly formed band started playing small bars in their hometown of Boston, locally popular songs such as Keep Away and Whatever soon brought them to the top of the hit charts in the Boston/New England area. The name stuck and they went by Godsmack from then on and we were aware of the Alice in Chains song but didnt really think much about it. In 1996, Tony Rombola and Joe DArco joined Godsmack as the guitarist and drummer, after Richards left upon learning he had a six-year-old child, in the same year, the band entered the studio for the first time, recording its first CD titled All Wound Up. The CD was recorded in just three days for $2,600, for the next two years, the band played throughout the Boston area. Eventually Godsmacks CD landed in the hands of Rocko, the night-time DJ for Boston radio station WAAF, the radio station put Keep Away into heavy rotation and the song rose to the number one spot at the station very quickly. Newbury Comics, a New England record store chain, agreed to sell the CD on consignment, shortly after the success of Keep Away, Godsmack went back into the studio and recorded a single titled Whatever, which became the new local favorite on WAAF. In an interview Sully Erna stated, We had been selling maybe 50 copies a month at the time WAAF picked up the album, All of a sudden we started moving over a thousand records a week. I was doing all this from my bedroom, after years of grinding away, things finally started taking off. In mid-1998, Universal/Republic Records signed the band to their label, Joe DArco was dismissed from the band. He was replaced by former drummer Tommy Stewart, who returned after expressing a desire to be in the band again, the bands first studio recording All Wound Up was re-mastered, and the finished self-titled debut CD album Godsmack was released to the public six weeks later
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Sphenic number
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In number theory, a sphenic number is a positive integer that is the product of three distinct prime numbers. A sphenic number is a product pqr where p, q and this definition is more stringent than simply requiring the integer to have exactly three prime factors. For instance,60 =22 ×3 ×5 has exactly 3 prime factors, the smallest sphenic number is 30 =2 ×3 ×5, the product of the smallest three primes. The first few numbers are 30,42,66,70,78,102,105,110,114,130,138,154,165. As of January 2016 the largest known number is × ×. It is the product of the three largest known primes, all sphenic numbers have exactly eight divisors. If we express the number as n = p ⋅ q ⋅ r, where p, q. For example,24 is not a number, but it has exactly eight divisors. All sphenic numbers are by definition squarefree, because the factors must be distinct. The Möbius function of any number is −1. The cyclotomic polynomials Φ n, taken over all sphenic numbers n, the first case of two consecutive sphenic integers is 230 = 2×5×23 and 231 = 3×7×11. The first case of three is 1309 = 7×11×17,1310 = 2×5×131, and 1311 = 3×19×23, there is no case of more than three, because every fourth consecutive positive integer is divisible by 4 = 2×2 and therefore not squarefree. The numbers 2013,2014, and 2015 are all sphenic, the next three consecutive sphenic years will be 2665,2666 and 2667. Semiprimes, products of two prime numbers
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Mertens function
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In number theory, the Mertens function is defined for all positive integers n as M = ∑ k =1 n μ where μ is the Möbius function. The function is named in honour of Franz Mertens and this definition can be extended to positive real numbers as follows, M = M. Less formally, M is the count of square-free integers up to x that have a number of prime factors. Because the Möbius function only takes the values −1,0, and +1, the Mertens conjecture went further, stating that there would be no x where the absolute value of the Mertens function exceeds the square root of x. The Mertens conjecture was proven false in 1985 by Andrew Odlyzko, however, the Riemann hypothesis is equivalent to a weaker conjecture on the growth of M, namely M = O. Since high values for M grow at least as fast as the root of x. Here, O refers to Big O notation, the true rate of growth of M is not known. An unpublished conjecture of Steve Gonek states that 0 < lim sup x → ∞ | M | x 5 /4 < ∞, probabilistic evidence towards this conjecture is given by Nathan Ng. Using the Euler product one finds that 1 ζ = ∏ p = ∑ n =1 ∞ μ n s where ζ is the Riemann zeta function and the product is taken over primes. Then, using this Dirichlet series with Perrons formula, one obtains,12 π i ∫ c − i ∞ c + i ∞ x s s ζ d s = M where c >1. Conversely, one has the Mellin transform 1 ζ = s ∫1 ∞ M x s +1 d x which holds for R e >1. A curious relation given by Mertens himself involving the second Chebyshev function is ψ = M log + M log + M log + ⋯. Assuming that there are not multiple non-trivial roots of ζ we have the formula by the residue theorem. Weyl conjectured that the Mertens function satisfied the approximate functional-differential equation y 2 − ∑ r =1 N B2 r. Another formula for the Mertens function is M = ∑ a ∈ F n e 2 π i a where F n is the Farey sequence of order n and this formula is used in the proof of the Franel–Landau theorem. M is the determinant of the n × n Redheffer matrix, using sieve methods similar to those used in prime counting, the Mertens function has been computed for all integers up to an increasing range of x. The Mertens function for all values up to x may be computed in O time. Combinatorial based algorithms can compute isolated values of M in O time, see A084237 for values of M at powers of 10
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Abundant number
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In number theory, an abundant number or excessive number is a number for which the sum of its proper divisors is greater than the number itself. The integer 12 is the first abundant number and its proper divisors are 1,2,3,4 and 6 for a total of 16. The amount by which the sum exceeds the number is the abundance, the number 12 has an abundance of 4, for example. A number n for which the sum of divisors σ>2n, or, equivalently, the sum of proper divisors s>n. The first 28 abundant numbers are,12,18,20,24,30,36,40,42,48,54,56,60,66,70,72,78,80,84,88,90,96,100,102,104,108,112,114,120, …. For example, the divisors of 24 are 1,2,3,4,6,8. Because 36 is more than 24, the number 24 is abundant and its abundance is 36 −24 =12. The smallest odd abundant number is 945, the smallest abundant number not divisible by 2 or by 3 is 5391411025 whose distinct prime factors are 5,7,11,13,17,19,23, and 29. An algorithm given by Iannucci in 2005 shows how to find the smallest abundant number not divisible by the first k primes. If A represents the smallest abundant number not divisible by the first k primes then for all ϵ >0 we have,2 − ϵ < ln A <2 + ϵ for sufficiently large k, infinitely many even and odd abundant numbers exist. The set of abundant numbers has a natural density, marc Deléglise showed in 1998 that the natural density of the set of abundant numbers and perfect numbers is between 0.2474 and 0.2480. Every multiple of a number is abundant. For example, every multiple of 6 is abundant because the divisors include 1, n/2, n/3, every multiple of an abundant number is abundant. For example, every multiple of 20 is abundant because n/2 + n/4 + n/5 + n/10 + n/20 = n + n/10, every integer greater than 20161 can be written as the sum of two abundant numbers. An abundant number which is not a number is called a weird number. An abundant number with abundance 1 is called a quasiperfect number, numbers whose sum of proper factors equals the number itself are called perfect numbers, while numbers whose sum of proper factors is less than the number itself are called deficient numbers. The abundancy index of n is the ratio σ/n, distinct numbers n1, n2. with the same abundancy index are called friendly numbers. The sequence of least numbers n such that σ > kn, in which a2 =12 corresponds to the first abundant number, if p = is a list of primes, then p is termed abundant if some integer composed only of primes in p is abundant