In mathematics, factorization or factoring consists of writing a number or another mathematical object as a product of several factors smaller or simpler objects of the same kind. For example, 3 × 5 is a factorization of the integer 15, is a factorization of the polynomial x2 – 4. Factorization is not considered meaningful within number systems possessing division, such as the real or complex numbers, since any x can be trivially written as × whenever y is not zero. However, a meaningful factorization for a rational number or a rational function can be obtained by writing it in lowest terms and separately factoring its numerator and denominator. Factorization was first considered by ancient Greek mathematicians in the case of integers, they proved the fundamental theorem of arithmetic, which asserts that every positive integer may be factored into a product of prime numbers, which cannot be further factored into integers greater than 1. Moreover, this factorization is unique up to the order of the factors.
Although integer factorization is a sort of inverse to multiplication, it is much more difficult algorithmically, a fact, exploited in the RSA cryptosystem to implement public-key cryptography. Polynomial factorization has been studied for centuries. In elementary algebra, factoring a polynomial reduces the problem of finding its roots to finding the roots of the factors. Polynomials with coefficients in the integers or in a field possess the unique factorization property, a version of the fundamental theorem of arithmetic with prime numbers replaced by irreducible polynomials. In particular, a univariate polynomial with complex coefficients admits a unique factorization into linear polynomials: this is a version of the fundamental theorem of algebra. In this case, the factorization can be done with root-finding algorithms; the case of polynomials with integer coefficients is fundamental for computer algebra. There are efficient computer algorithms for computing factorizations within the ring of polynomials with rational number coefficients.
A commutative ring possessing the unique factorization property is called a unique factorization domain. There are number systems, such as certain rings of algebraic integers, which are not unique factorization domains. However, rings of algebraic integers satisfy the weaker property of Dedekind domains: ideals factor uniquely into prime ideals. Factorization may refer to more general decompositions of a mathematical object into the product of smaller or simpler objects. For example, every function may be factored into the composition of a surjective function with an injective function. Matrices possess many kinds of matrix factorizations. For example, every matrix has a unique LUP factorization as a product of a lower triangular matrix L with all diagonal entries equal to one, an upper triangular matrix U, a permutation matrix P. By the fundamental theorem of arithmetic, every integer greater than 1 has a unique factorization into prime numbers, which are those integers which cannot be further factorized into the product of integers greater than one.
For computing the factorization of an integer n, one needs an algorithm for finding a divisor q of n or deciding that n is prime. When such a divisor is found, the repeated application of this algorithm to the factors q and n / q gives the complete factorization of n. For finding a divisor q of n, if any, it suffices to test all values of q such that 1 < q and q2 ≤ n. In fact, if r is a divisor of n such that r2 > n q = n / r is a divisor of n such that q2 ≤ n. If one tests the values of q in increasing order, the first divisor, found is a prime number, the cofactor r = n / q cannot have any divisor smaller than q. For getting the complete factorization, it suffices thus to continue the algorithm by searching a divisor of r, not smaller than q and not greater than √r. There is no need to test all values of q for applying the method. In principle, it suffices to test only prime divisors; this needs to have a table of prime numbers that may be generated for example with the sieve of Eratosthenes.
As the method of factorization does the same work as the sieve of Eratosthenes, it is more efficient to test for a divisor only those numbers for which it is not clear whether they are prime or not. One may proceed by testing 2, 3, 5, the numbers > 5, whose last digit is 1, 3, 7, 9 and the sum of digits is not a multiple of 3. This method is inefficient for larger integers. For example, Pierre de Fermat was unable to discover that the 6th Fermat number 1 + 2 2 5 = 1 + 2 32 = 4 294 967 297 is not a prime number. In fact, applying the above method would require more than 10000 divisions, for a number that has 10 decimal digits. There are more efficient factoring algorithms; however they remain inefficient, as, with the present state of the art, one cannot factorize with the more powerful computers, a number of 500 decimal digits, the product of two randomly chosen prime numbers. This insures the security of the RSA cryptosystem, used for secure internet communication. For fa
Alexander Bellos is a British writer and broadcaster. He is the author of books about Brazil and mathematics, as well as having a column in The Guardian newspaper. Alex Bellos grew up in Edinburgh and Southampton, he was educated at Hampton Park Comprehensive School and Richard Taunton Sixth Form College in Southampton. He went on to study mathematics and philosophy at Corpus Christi College, where he was the editor of the student paper Cherwell. Bellos first job was working for The Argus in Brighton before moving to The Guardian in London. From 1998 to 2003 he was South America correspondent of The Guardian, wrote Futebol: the Brazilian Way of Life; the book was well received in the UK, where it was nominated for sports book of the year at the British Book Awards. In the US, it was included as one of Publishers Weekly's books of the year, they wrote: “Compelling... Alternately funny and dark... Bellos offers a cast of characters as colorful as a Carnival parade”. In 2006, he ghostwrote Pelé: The Autobiography, about the soccer player Pelé, a number one best-seller in the UK.
Returning to live in the UK, Bellos decided to write about mathematics. The book Alex's Adventures in Numberland was published in 2010 and spent four months in The Sunday Times' top ten best-sellers' list; the Daily Telegraph described the book as a "mathematical wonder that will leave you hooked on numbers." The book was shortlisted for three awards in the UK, including the BBC Samuel Johnson Prize for Non-Fiction 2010. The Guardian reported. Chairman of the judges Evan Davis broke with protocol to discuss their deliberations: " was a book everyone thought would be nice if it won, because it would be good for people to read a maths book; some of us wished. If we'd taken the view that this is a book everyone ought to read it might have gone that way."Several translations of the book have been published. The Italian version, Il meraviglioso mondo dei numeri, won both the €10,000 Galileo Prize for science books and the 2011 Peano Prize for mathematics books. In the United States, the book was given.
Alex Through The Looking-Glass: How Life Reflects Numbers and Numbers Reflect Life was published in 2014 and received positive reviews. The Daily Telegraph wrote: “If anything, Looking Glass is a better work than Numberland – it feels more immediate, more relevant and more fun.” Its US title was The Grapes of Math, about which The New York Times said Bellos was: “a charming and eloquent guide to math’s mysteries…There’s an interesting fact or mathematical obsessive on every page. And for its witty flourishes, it’s never shallow. Bellos doesn’t shrink from delving into equations, which should delight aficionados who relish those kinds of details.” Bellos presented the BBC TV series Inside Out Brazil, authored the documentary Et Dieu créa…le foot, about football in the Amazon rainforest, shown on the National Geographic Channel. His short films on the Amazon have appeared on More4 and Al Jazeera, he appears on the BBC talking about mathematics. His Radio 4 documentary Nirvana by Numbers was shortlisted for best radio programme in the 2014 Association of British Science Writers Awards.
Futebol: The Brazilian Way of Life Pelé, The Autobiography Football School Season 1 with Ben Lyttleton and illustrated by Spike Gerrell Football School Season 2 with Ben Lyttleton and illustrated by Spike Gerrell Alex's Adventures in Numberland/Here's Looking at Euclid Alex Through the Looking-Glass/The Grapes of Math Snowflake Seashell Star/Patterns of the Universe with Edmund Harriss – colouring book Can You Solve My Problems? – puzzle book Visions of Numberland/Patterns of the Universe with Edmund Harriss – colouring book Puzzle Ninja – Japanese puzzle book 2017 Shortlisted for the Blue Peter Book Award for Best Book with Facts for Football School: Where Football Explains the World 2012 Premio Letterario Galileo, winner, Il meraviglioso mondo dei numeri 2012 Peano Prize, winner, Il meraviglioso mondo dei numeri 2011 Shortlisted for the Royal Society Prizes for Science Books for Alex's Adventures in Numberland 2010 Amazon.com, Best Books of 2010: Science for Here's Looking at Euclid 2010 Shortlisted for the British Book Awards, Non-Fiction Book of the Year for Alex's Adventures in Numberland 2010 Shortlisted for the BBC Samuel Johnson Prize for Non-Fiction for Alex's Adventures in Numberland 2004 Shortlisted for British Book Awards, Sports Book of the Year for Futebol: The Brazilian Way of Life 2003 Shortlisted for National Sporting Club British Sports Book Awards Futebol: The Brazilian Way of Life Bellos lives in London and is married with children.
His father David Bellos is a translator and academic and his mother is Hungarian
In mathematics, the natural numbers are those used for counting and ordering. In common mathematical terminology, words colloquially used for counting are "cardinal numbers" and words connected to ordering represent "ordinal numbers"; the natural numbers can, at times, appear as a convenient set of codes. Some definitions, including the standard ISO 80000-2, begin the natural numbers with 0, corresponding to the non-negative integers 0, 1, 2, 3, …, whereas others start with 1, corresponding to the positive integers 1, 2, 3, …. 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; the natural numbers are a basis from which many other number sets may be built by extension: the integers, by including the neutral element 0 and an additive inverse for each nonzero natural number n. These chains of extensions make the natural numbers canonically embedded in the other number systems.
Properties of the natural 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. In common language, for example in primary school, natural numbers may be called counting numbers both to intuitively exclude the negative integers and zero, to contrast the discreteness of counting to the continuity of measurement, established by the real numbers; the most primitive method of representing a natural number is to put down a mark for each object. A set of objects could be tested for equality, excess or shortage, by striking out a mark and removing an object from the set; 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, 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, 6 ones. The Babylonians had a place-value system based on the numerals for 1 and 10, using base sixty, so that the symbol for sixty was the same as the symbol for one, its value being determined from context. A much 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, but they omitted such a digit when it would have been the last symbol in the number. 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. However, 0 had been used as a number in the medieval computus, beginning with Dionysius Exiguus in 525, without being denoted by a numeral; the first systematic study of numbers as abstractions is credited to the Greek philosophers Pythagoras and Archimedes.
Some Greek mathematicians treated the number 1 differently than larger numbers, sometimes not as a number at all. Independent studies occurred at around the same time in India and Mesoamerica. In 19th century Europe, there was mathematical and philosophical discussion about the exact nature of the natural numbers. A school of Naturalism stated that the natural 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, all else is the work of man". 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 natural but a consequence of definitions. Two classes of such formal definitions were constructed. Set-theoretical definitions of natural numbers were initiated by Frege and he defined a natural number as the class of all sets that are in one-to-one correspondence with a particular set, but this definition turned out to lead to paradoxes including Russell's paradox.
Therefore, this formalism was modified so that a natural number is defined as a particular set, any set that can be put into one-to-one correspondence with that set is said to have that number of elements. The second class of definitions was introduced by Charles Sanders Peirce, refined by Richard Dedekind, further explored by Giuseppe Peano, it is based on an axiomatization of the properties of ordinal numbers: each natural number has a
100 or one hundred is the natural number following 99 and preceding 101. In medieval contexts, it may be described as the short hundred or five score in order to differentiate the English and Germanic use of "hundred" to describe the long hundred of six score or 120. 100 is the square of 10. The standard SI prefix for a hundred is "hecto-". 100 is the basis of percentages. 100 is the sum of the first nine prime numbers, as well as the sum of some pairs of prime numbers e.g. 3 + 97, 11 + 89, 17 + 83, 29 + 71, 41 + 59, 47 + 53. 100 is the sum of the cubes of the first four integers. This is related by Nicomachus's theorem to the fact that 100 equals the square of the sum of the first four integers: 100 = 102 = 2.26 + 62 = 100, thus 100 is a Leyland number.100 is an 18-gonal number. It is divisible by 25, the number of primes below it, it can not be expressed as the difference between any integer and the total of coprimes below it, making it a noncototient. It can be expressed as a sum of some of its divisors.
100 is a Harshad number in base 10, in base 4, in that base it is a self-descriptive number. There are 100 prime numbers whose digits are in ascending order. 100 is the smallest number. One hundred is the atomic number of fermium, an actinide and the first of the heavy metals that cannot be created through neutron bombardment. On the Celsius scale, 100 degrees is the boiling temperature of pure water at sea level; the Kármán line lies at an altitude of 100 kilometres above the Earth's sea level and is used to define the boundary between Earth's atmosphere and outer space. There are 100 blasts of the Shofar heard in the service of the Jewish New Year. A religious Jew is expected to utter at least 100 blessings daily. In the Hindu book of the Mahabharata, the king Dhritarashtra had 100 sons known as the Kauravas; the United States Senate has 100 Senators. Most of the world's currencies are divided into 100 subunits; the 100 Euro banknotes feature a picture of a Rococo gateway on the obverse and a Baroque bridge on the reverse.
The U. S. hundred-dollar bill has Benjamin Franklin's portrait. S. bill in print. American savings bonds of $100 have Thomas Jefferson's portrait, while American $100 treasury bonds have Andrew Jackson's portrait. One hundred is also: The number of years in a century; the number of pounds in an American short hundredweight. In Greece, India and Nepal, 100 is the police telephone number. In Belgium, 100 is the firefighter telephone number. In United Kingdom, 100 is the operator telephone number; the HTTP status code indicating that the client should continue with its request. The 100 The age at which a person becomes a centenarian; the number of yards in an American football field. The number of runs required for a cricket batsman to score a significant milestone; the number of points required for a snooker player to score a century break, a significant milestone. The record number of points scored in one NBA game by a single player, set by Wilt Chamberlain of the Philadelphia Warriors on March 2, 1962.
1 vs. 100 AFI's 100 Years... Hundred Hundred Hundred Days Hundred Years' War List of highways numbered 100 Top 100 Greatest 100 Wells, D; the Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group.: 133 Chisholm, Hugh, ed.. "Hundred". Encyclopædia Britannica. Cambridge University Press. On the Number 100
In mathematics and computing, hexadecimal is a positional numeral system with a radix, or base, of 16. It uses sixteen distinct symbols, most the symbols "0"–"9" to represent values zero to nine, "A"–"F" to represent values ten to fifteen. Hexadecimal numerals are used by computer system designers and programmers, as they provide a more human-friendly representation of binary-coded values; each hexadecimal digit represents four binary digits known as a nibble, half a byte. For example, a single byte can have values ranging from 0000 0000 to 1111 1111 in binary form, which can be more conveniently represented as 00 to FF in hexadecimal. In mathematics, a subscript is used to specify the radix. For example the decimal value 10,995 would be expressed in hexadecimal as 2AF316. In programming, a number of notations are used to support hexadecimal representation involving a prefix or suffix; the prefix 0x is used in C and related languages, which would denote this value by 0x2AF3. Hexadecimal is used in the transfer encoding Base16, in which each byte of the plaintext is broken into two 4-bit values and represented by two hexadecimal digits.
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; some authors prefer a text subscript, such as 159decimal and 159hex, or 159h. In linear text systems, such as those used in most computer programming environments, a variety of methods have arisen: In URIs, character codes are written as hexadecimal pairs prefixed with %: http://www.example.com/name%20with%20spaces where %20 is the space character, ASCII code point 20 in hex, 32 in decimal. In XML and XHTML, characters can be expressed as hexadecimal numeric character references using the notation
ode, thus ’. In the Unicode standard, a character value is represented with U+ followed by the hex value, e.g. U+20AC is the Euro sign. Color references in HTML, CSS and X Window can be expressed with six hexadecimal digits prefixed with #: white, for example, is represented #FFFFFF.
CSS allows 3-hexdigit abbreviations with one hexdigit per component: #FA3 abbreviates #FFAA33. Unix shells, AT&T assembly language and the C programming language use the prefix 0x for numeric constants represented in hex: 0x5A3. Character and string constants may express character codes in hexadecimal with the prefix \x followed by two hex digits:'\x1B' represents the Esc control character. To output an integer as hexadecimal with the printf function family, the format conversion code %X or %x is used. In MIME quoted-printable encoding, characters that cannot be represented as literal ASCII characters are represented by their codes as two hexadecimal digits prefixed by an equal to sign =, as in Espa=F1a to send "España". In Intel-derived assembly languages and Modula-2, hexadecimal is denoted with a suffixed H or h: FFh or 05A3H; some implementations require a leading zero when the first hexadecimal digit character is not a decimal digit, so one would write 0FFh instead of FFh Other assembly languages, Delphi, some versions of BASIC, GameMaker Language and Forth use $ as a prefix: $5A3.
Some assembly languages use the notation H'ABCD'. Fortran 95 uses Z'ABCD'. Ada and VHDL enclose hexadecimal numerals in based "numeric quotes": 16#5A3#. For bit vector constants VHDL uses the notation x"5A3". Verilog represents hexadecimal constants in the form 8'hFF, where 8 is the number of bits in the value and FF is the hexadecimal constant; 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: AA213FD51B3801043FBC... Common Lisp uses the prefixes # 16r. Setting the variables *read-base* and *print-base* to 16 can be 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, when the input or output base has been changed to 16. 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 ALGOL 68 uses the prefix 16r to denote hexadecimal numbers: 16r5a3. Binary and octal numbers can be specified similarly; the most common format for hexadecimal on IBM mainframes and midrange computers running the traditional OS's is X'5A3', is used in Assembler, PL/I, COBOL, JCL, scripts and other places. This format was common on
In mathematics, a negative number is a real number, less than zero. Negative numbers represent opposites. If positive represents a movement to the right, negative represents a movement to the left. If positive represents above sea level negative represents below sea level. If positive represents a deposit, negative represents a withdrawal, they are used to represent the magnitude of a loss or deficiency. A debt, owed may be thought of as a negative asset, a decrease in some quantity may be thought of as a negative increase. If a quantity may have either of two opposite senses 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 sense idea of an opposite is reflected in arithmetic.
For example, − = 3 because the opposite of an opposite is the original value. Negative numbers are written with a minus sign in front. For example, −3 represents a negative quantity with a magnitude of three, is pronounced "minus three" or "negative three". To help tell the difference between a subtraction operation and a negative number the negative sign is placed higher than the minus sign. Conversely, a number, 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 negative. The positive whole numbers are referred to as natural numbers, while the positive and negative whole numbers are referred to as integers. In bookkeeping, amounts owed are represented by red numbers, or a number in parentheses, as an alternative notation to represent negative numbers. Negative numbers appeared for the first time in history in the Nine Chapters on the Mathematical Art, which in its present form dates from the period of the Chinese Han Dynasty, but may well contain much older material.
Liu Hui established rules for 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 negative numbers around the middle of the 19th century. Prior to the concept of negative numbers, mathematicians such as Diophantus considered negative solutions to problems "false" and equations requiring negative solutions were described as absurd; some mathematicians like Leibniz agreed that negative numbers were false, but still used them in calculations. Negative numbers can be thought of as resulting from the subtraction of a larger 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.
For example, 5 − 8 = −3since 8 − 5 = 3. The relationship between negative numbers, positive numbers, zero is expressed in the form of a number line: Numbers appearing farther to the right on this line are greater, while numbers appearing farther to the left are less, thus zero appears in the middle, with the positive numbers to the right and the negative numbers to the left. Note that a negative number with greater magnitude is considered less. For example though 8 is greater than 5, written 8 > 5negative 8 is considered to be less than negative 5: −8 < −5. It follows that any negative number is less than any positive number, so −8 < 5 and −5 < 8. In the context of negative numbers, a number, greater than zero is referred to as positive, thus every real number other than zero is either positive or negative, while zero itself is not considered to have a sign. Positive numbers are sometimes written with a plus sign in front, e.g. +3 denotes a positive three. Because zero is neither positive nor negative, the term nonnegative is sometimes used to refer to a number, either positive or zero, while nonpositive is used to refer to a number, either negative or zero.
Zero is a neutral number. Goal difference in association football and hockey. Plus-minus differential in ice hockey: the difference in total goals scored for the team and against the team when a particular player is on the ice is the player’s +/− rating. Players can have a negative rating. Run differential in baseball: the run differential is negative if the team allows more runs than they scored. British football clubs are deducted points if they enter administration, thus have a negative points total until they have earned at least that many points that season. Lap times in Formula 1 may be given as the difference compared to a previous lap, will be positive if slower and negative if faster. In some athletics events, such as sprint races, the hurdles, the triple jump and the long jump, the wind assistance is measured and recorde
Wikipedia is a multilingual online encyclopedia with free content and no ads, based on open collaboration through a model of content edit by web-based applications like web browsers, called wiki. It is the largest and most popular general reference work on the World Wide Web, is one of the most popular websites by Alexa rank as of April 2019, it is owned and supported by the Wikimedia Foundation, a non-profit organization that operates on money it receives from donors to remain ad free. Wikipedia was launched on January 2001, by Jimmy Wales and Larry Sanger. Sanger coined its name, as a portmanteau of wiki and "encyclopedia". An English-language encyclopedia, versions in other languages were developed. With 5,838,942 articles, the English Wikipedia is the largest of the more than 290 Wikipedia encyclopedias. Overall, Wikipedia comprises more than 40 million articles in 301 different languages and by February 2014 it had reached 18 billion page views and nearly 500 million unique visitors per month.
In 2005, Nature published a peer review comparing 42 hard science articles from Encyclopædia Britannica and Wikipedia and found that Wikipedia's level of accuracy approached that of Britannica, although critics suggested that it might not have fared so well in a similar study of a random sampling of all articles or one focused on social science or contentious social issues. The following year, Time magazine stated that the open-door policy of allowing anyone to edit had made Wikipedia the biggest and the best encyclopedia in the world, was a testament to the vision of Jimmy Wales. Wikipedia has been criticized for exhibiting systemic bias, for presenting a mixture of "truths, half truths, some falsehoods", for being subject to manipulation and spin in controversial topics. In 2017, Facebook announced that it would help readers detect fake news by suitable links to Wikipedia articles. YouTube announced a similar plan in 2018. Other collaborative online encyclopedias were attempted before Wikipedia, but none were as successful.
Wikipedia began as a complementary project for Nupedia, a free online English-language encyclopedia project whose articles were written by experts and reviewed under a formal process. It was founded on March 2000, under the ownership of Bomis, a web portal company, its main figures were Bomis CEO Jimmy Wales and Larry Sanger, editor-in-chief for Nupedia and Wikipedia. Nupedia was licensed under its own Nupedia Open Content License, but before Wikipedia was founded, Nupedia switched to the GNU Free Documentation License at the urging of Richard Stallman. Wales is credited with defining the goal of making a publicly editable encyclopedia, while Sanger is credited with the strategy of using a wiki to reach that goal. On January 10, 2001, Sanger proposed on the Nupedia mailing list to create a wiki as a "feeder" project for Nupedia; the domains wikipedia.com and wikipedia.org were registered on January 12, 2001 and January 13, 2001 and Wikipedia was launched on January 15, 2001, as a single English-language edition at www.wikipedia.com, announced by Sanger on the Nupedia mailing list.
Wikipedia's policy of "neutral point-of-view" was codified in its first months. Otherwise, there were few rules and Wikipedia operated independently of Nupedia. Bomis intended to make Wikipedia a business for profit. Wikipedia gained early contributors from Nupedia, Slashdot postings, web search engine indexing. Language editions were created, with a total of 161 by the end of 2004. Nupedia and Wikipedia coexisted until the former's servers were taken down permanently in 2003, its text was incorporated into Wikipedia; the English Wikipedia passed the mark of two million articles on September 9, 2007, making it the largest encyclopedia assembled, surpassing the 1408 Yongle Encyclopedia, which had held the record for 600 years. Citing fears of commercial advertising and lack of control in Wikipedia, users of the Spanish Wikipedia forked from Wikipedia to create the Enciclopedia Libre in February 2002; these moves encouraged Wales to announce that Wikipedia would not display advertisements, to change Wikipedia's domain from wikipedia.com to wikipedia.org.
Though the English Wikipedia reached three million articles in August 2009, the growth of the edition, in terms of the numbers of new articles and of contributors, appears to have peaked around early 2007. Around 1,800 articles were added daily to the encyclopedia in 2006. A team at the Palo Alto Research Center attributed this slowing of growth to the project's increasing exclusivity and resistance to change. Others suggest that the growth is flattening because articles that could be called "low-hanging fruit"—topics that merit an article—have been created and built up extensively. In November 2009, a researcher at the Rey Juan Carlos University in Madrid found that the English Wikipedia had lost 49,000 editors during the first three months of 2009; the Wall Street Journal cited the array of rules applied to editing and disputes related to such content among the reasons for this trend. Wales disputed these claims in 2009, denying the decline and questioning the methodology of the study. Two years in 2011, Wales acknowledged the presence of a slight decline, noting a decrease from "a little more than 36,000 writers" in June 2010 to 35,800 in June 2011.
In the same interview, Wales claimed the number of editors was "stable and sustainable". A 2013 article titled; the article revealed