In predicate logic, an existential quantification is the predication^[1] of a property or relation to at least one member of the domain. It is denoted by the logical operator symbol ∃ (pronounced "there exists" or "for some"), which is called the existential quantifier. Existential quantification is distinct from universal quantification ("for all"), which asserts that the property or relation holds for any members of the domain.

Symbols are encoded U+2203 ∃ there exists (HTML: ∃ ∃ as a mathematical symbol) and U+2204 ∄ there does not exist (HTML: ∄).

Basics[link]

Consider a formula that states that some natural number multiplied by itself is 25.

0·0 = 25, or 1·1 = 25, or 2·2 = 25, or 3·3 = 25, and so on.

This would seem to be a logical disjunction because of the repeated use of "or". However, the "and so on" makes this impossible to integrate and to interpret as a disjunction in formal logic. Instead, the statement could be rephrased more formally as

For some natural number n, n·n = 25.

This is a single statement using existential quantification.

This statement is more precise than the original one, as the phrase "and so on" does not necessarily include all natural numbers, and nothing more. Since the domain was not stated explicitly, the phrase could not be interpreted formally. In the quantified statement, on the other hand, the natural numbers are mentioned explicitly.

This particular example is true, because 5 is a natural number, and when we substitute 5 for n, we produce "5·5 = 25", which is true. It does not matter that "n·n = 25" is only true for a single natural number, 5; even the existence of a single solution is enough to prove the existential quantification true. In contrast, "For some even number n, n·n = 25" is false, because there are no even solutions.

The domain of discourse, which specifies which values the variable n is allowed to take, is therefore of critical importance in a statement's trueness or falseness. Logical conjunctions are used to restrict the domain of discourse to fulfill a given predicate. For example:

For some positive odd number n, n·n = 25

is logically equivalent to

For some natural number n, n is odd and n·n = 25.

Here, "and" is the logical conjunction.

In symbolic logic, "∃" (a backwards letter "E" in a sans-serif font) is used to indicate existential quantification.^[2] Thus, if P(a, b, c) is the predicate "a·b = c" and Failed to parse (Missing texvc executable; please see math/README to configure.): \mathbb{N}

is the set of natural numbers, then

Failed to parse (Missing texvc executable; please see math/README to configure.): \exists{n}{\in}\mathbb{N}\, P(n,n,25)

is the (true) statement

For some natural number n, n·n = 25.

Similarly, if Q(n) is the predicate "n is even", then

Failed to parse (Missing texvc executable; please see math/README to configure.): \exists{n}{\in}\mathbb{N}\, \big(Q(n)\;\!\;\! {\wedge}\;\!\;\! P(n,n,25)\big)

is the (false) statement

For some natural number n, n is even and n·n = 25.

In mathematics, the proof of a "some" statement may be achieved either by a constructive proof, which exhibits an object satisfying the "some" statement, or by a nonconstructive proof which shows that there must be such an object but without exhibiting one.

Properties[link]

Negation[link]

A quantified propositional function is a statement; thus, like statements, quantified functions can be negated. The Failed to parse (Missing texvc executable; please see math/README to configure.): \lnot\   symbol is used to denote negation.

For example, if P(x) is the propositional function "x is between 0 and 1", then, for a domain of discourse X of all natural numbers, the existential quantification "There exists a natural number x which is between 0 and 1" is symbolically stated:

Failed to parse (Missing texvc executable; please see math/README to configure.): \exists{x}{\in}\mathbf{X}\, P(x)

This can be demonstrated to be irrevocably false. Truthfully, it must be said, "It is not the case that there is a natural number x that is between 0 and 1", or, symbolically:

Failed to parse (Missing texvc executable; please see math/README to configure.): \lnot\ \exists{x}{\in}\mathbf{X}\, P(x)

.

If there is no element of the domain of discourse for which the statement is true, then it must be false for all of those elements. That is, the negation of

Failed to parse (Missing texvc executable; please see math/README to configure.): \exists{x}{\in}\mathbf{X}\, P(x)

is logically equivalent to "For any natural number x, x is not between 0 and 1", or:

Failed to parse (Missing texvc executable; please see math/README to configure.): \forall{x}{\in}\mathbf{X}\, \lnot P(x)

Generally, then, the negation of a propositional function's existential quantification is a universal quantification of that propositional function's negation; symbolically,

Failed to parse (Missing texvc executable; please see math/README to configure.): \lnot\ \exists{x}{\in}\mathbf{X}\, P(x) \equiv\ \forall{x}{\in}\mathbf{X}\, \lnot P(x)

A common error is stating "all persons are not married" (i.e. "there exists no person who is married") when "not all persons are married" (i.e. "there exists a person who is not married") is intended:

Failed to parse (Missing texvc executable; please see math/README to configure.): \lnot\ \exists{x}{\in}\mathbf{X}\, P(x) \equiv\ \forall{x}{\in}\mathbf{X}\, \lnot P(x) \not\equiv\ \lnot\ \forall{x}{\in}\mathbf{X}\, P(x) \equiv\ \exists{x}{\in}\mathbf{X}\, \lnot P(x)

Negation is also expressible through a statement of "for no", as opposed to "for some":

Failed to parse (Missing texvc executable; please see math/README to configure.): \nexists{x}{\in}\mathbf{X}\, P(x) \equiv \lnot\ \exists{x}{\in}\mathbf{X}\, P(x)

Unlike the universal quantifier, the existential quantifier distributes over logical disjunctions:

Failed to parse (Missing texvc executable; please see math/README to configure.): \exists{x}{\in}\mathbf{X}\, P(x) \or Q(x) \to\ (\exists{x}{\in}\mathbf{X}\, P(x) \or \exists{x}{\in}\mathbf{X}\, Q(x))

Rules of Inference[link]

A rule of inference is a rule justifying a logical step from hypothesis to conclusion. There are several rules of inference which utilize the existential quantifier.

Existential introduction (∃I) concludes that, if the propositional function is known to be true for a particular element of the domain of discourse, then it must be true that there exists an element for which the proposition function is true. Symbolically,

Failed to parse (Missing texvc executable; please see math/README to configure.): P(a) \to\ \exists{x}{\in}\mathbf{X}\, P(x)

The reasoning behind existential elimination (∃E) is as follows: If it is given that there exists an element for which the proposition function is true, and if a conclusion can be reached by giving that element an arbitrary name, that conclusion is necessarily true, as long as it does not contain the name. Symbolically, for an arbitrary c and for a proposition Q in which c does not appear:

Failed to parse (Missing texvc executable; please see math/README to configure.): \exists{x}{\in}\mathbf{X}\, P(x) \to\ ((P(c) \to\ Q) \to\ Q)

Failed to parse (Missing texvc executable; please see math/README to configure.): P(c) \to\ Q

must be true for all values of c over the same domain X; else, the logic does not follow: If c is not arbitrary, and is instead a specific element of the domain of discourse, then stating P(c)  might unjustifiably give more information about that object.

The empty set[link]

The formula Failed to parse (Missing texvc executable; please see math/README to configure.): \exists {x}{\in}\emptyset \, P(x)

is always false, regardless of P(x). This is because Failed to parse (Missing texvc executable; please see math/README to configure.): \emptyset
denotes the empty set, and no x of any description – let alone an x fulfilling a given predicate P(x) – exist in the empty set. See also vacuous truth.

See also[link]

• Uniqueness quantification
• Quantifiers
• First-order logic

Notes[link]

1. ^ The term "predication" in grammar means the predicate of a sentence which refers to subject and is an adverb or adjective, or equivalent, that describes an attribute of the subject. In logic, "predication" is a declaration (or assertion) that is claimed to be self-evident and can be assumed as the basis for argument.
2. ^ This symbol is also known as the existential operator. It is sometimes represented with V.

References[link]

• Hinman, P. (2005). Fundamentals of Mathematical Logic. A K Peters. ISBN 1-56881-262-0. 

Justin Bieber
Justin Bieber at the NRJ Music Awards in Cannes, France in 2012
Background information
Birth name	Justin Drew Bieber[1]
Born	(1994-03-01) March 1, 1994 (age 18)[2] London, Ontario, Canada
Origin	Stratford, Ontario, Canada
Genres	Pop, R&B, teen pop[3][4][5]
Occupations	Singer-songwriter, musician, actor
Instruments	Vocals, guitar, piano, percussion,[6] trumpet[7]
Years active	2008–present
Labels	Island, RBMG
Associated acts	Usher, Ludacris
Website	justinbiebermusic.com

Justin Drew Bieber ( /ˈbiːbər/ BEE-bər, born March 1, 1994)^[2] is a Canadian Pop/R&B singer-songwriter, musician, and actor.^[3][5] Bieber was discovered in 2008 by Scooter Braun,^[8] who came across Bieber's videos on YouTube and later became his manager. Braun arranged for him to meet with Usher in Atlanta, Georgia, and Bieber was soon signed to Raymond Braun Media Group (RBMG), a joint venture between Braun and Usher,^[9] and then to a recording contract with Island Records offered by L.A. Reid.^[6][10] Bieber's debut single, "One Time", was released in 2009 and peaked in the top twenty in Canada and charted in the top thirty in several international markets. His debut album, the seven-track EP My World, followed in November 2009, and was soon certified platinum in the United States. He became the first artist to have seven songs from a debut album chart on the Billboard Hot 100.^[11]

Bieber's first full-length studio album, My World 2.0, was released in March 2010. It debuted at number one or within the top ten in several countries and was certified platinum in the United States. It was preceded by the worldwide top-ten single, "Baby". The music video of "Baby" is currently ranked as the most viewed and most discussed YouTube video.^[12] Bieber followed up the release of his debut album with his first headlining tour, the My World Tour, the remix albums My Worlds Acoustic and Never Say Never – The Remixes, and the 3D biopic-concert film Justin Bieber: Never Say Never, that nearly matched the record for the biggest opening weekend gross for a concert-film. Bieber released his second studio album, Under the Mistletoe, in November 2011, which debuted at number one on the Billboard 200. Bieber has received numerous awards, including Artist of the Year at the 2010 American Music Awards, and has been nominated for such awards as Best New Artist and Best Pop Vocal Album at the 53rd Grammy Awards. In 2012, Bieber was named Forbes 3rd most powerful celebrity in the world, earning $55 million. As of May 2012, Bieber has sold 15 million albums.^[13]

Early life[link]

Bieber was born on March 1, 1994, in London, Ontario in St Joseph's Hospital,^[14][15] and was raised in Stratford, Ontario.^[16] Bieber's mother, Patricia Lynn "Pattie" Mallette, was 18 years old when she became pregnant. Mallette, originally from Stratford, raised her son with the help of her parents, Bruce and Diane.^[17] Mallette worked a series of low-paying office jobs, raising Bieber as a single mother in low-income housing. Bieber has maintained contact with his father, Jeremy Jack Bieber, who married another woman and had two children.^[18][19][20] Bieber's great-grandfather was from Germany.^[21] Bieber's mother's ancestry is French Canadian.^[22] Bieber attended a French immersion elementary school in Stratford called Jeanne Sauvé Catholic School.^[17]

During his childhood, Bieber was interested in hockey, soccer, and chess; he often kept his musical aspirations to himself.^[18] As he grew up, Bieber taught himself to play the piano, drums, guitar, and trumpet.^[16][23] In early 2007, when he was twelve, Bieber sang Ne-Yo's "So Sick" for a local singing competition in Stratford and was placed second.^[6][23] Mallette posted a video of the performance on YouTube for their family and friends to see. She continued to upload videos of Bieber singing covers of various R&B songs, and Bieber's popularity on the site grew.^[10] Chris Hicks, Bieber's A&R at Island/Def Jam, explained the young artist's huge online following to HitQuarters by saying:

"He was doing something different. He was an attractive white kid singing very soulful R&B hits. That set him apart immediately from anyone in his range because no one was covering or singing these kind of records. But equally important was that you believed in these songs – it was real. And you wanted to hear more."^[24]

Career[link]

[edit] 2008–09: Discovery and My World

While searching for videos of a different singer, Scooter Braun, a former marketing executive of So So Def, clicked on one of Bieber's 2007 videos by accident.^[18] Impressed, Braun tracked down the theater Bieber was performing in, located Bieber's school, and finally contacted Mallette. Mallette was reluctant because of Braun's Jewish religion; she remembered praying, "God, I gave him to you. You could send me a Christian man, a Christian label! ... you don’t want this Jewish kid to be Justin’s man, do you?"^[18] However, after praying with her church elders and receiving their encouragement, she permitted Braun to fly Bieber, then 13,^[10] to Atlanta, Georgia, to record demo tapes.^[18] A week after arriving, Bieber sang for R&B singer/songwriter Usher.^[25] Bieber was soon signed to Raymond Braun Media Group (RBMG), a joint venture between Braun and Usher.^[9] Justin Timberlake was also reportedly in the running to sign Bieber, but lost the bidding war to Usher.^[9][26] Usher then sought assistance in finding a label home for the artist from then manager Chris Hicks, who helped engineer an audition with his contact Antonio L.A. Reid of Island Def Jam Music Group.^[24] Reid signed Bieber to Island Records in October 2008 (resulting in a joint venture between RBMG and Island Records) and appointed Hicks as executive Vice-President of Def Jam where he would be able manage Bieber's career at the label.^{[6][9][10][24]} At that point, Bieber and his mother moved to Atlanta temporarily, also the home of Usher and Braun, to record and get counseling from Braun.^[9] Braun became Bieber's manager.^[10]

Bieber in September 2009 at the Nintendo World Store

Bieber's first single, "One Time", was released to radio while Bieber was still recording his debut album.^[27] The song reached number 12 on the Canadian Hot 100 during its first week of release in July 2009,^[10] and later peaked at number 17 on the Billboard Hot 100. During fall 2009 it had success in international markets.^[28] The song was certified Platinum in Canada and the US and Gold in Australia and New Zealand.^[29][30][31] Bieber's first release, an extended play entitled My World, was released on November 17, 2009. The album's second single, "One Less Lonely Girl", and two promo singles, "Love Me", and "Favorite Girl", were released exclusively on the iTunes store and charted within the top forty of the Billboard Hot 100.^[28] "One Less Lonely Girl" was later also released to radio and peaked within the top fifteen in Canada and the US, being certified Gold in the latter.^[28] My World was eventually certified Platinum in the US and Double Platinum in both Canada and the UK.^[31][32][33] To promote the album, Bieber performed on several live shows such as mtvU's VMA 09 Tour, European program The Dome, YTV's The Next Star, The Today Show,^[34][35] The Wendy Williams Show, Lopez Tonight, The Ellen DeGeneres Show, It's On with Alexa Chung, Good Morning America, Chelsea Lately, and BET's 106 & Park with Rihanna. Bieber also guest starred in an episode of True Jackson, VP in late 2009.^[36]

Bieber performed Stevie Wonder's "Someday at Christmas" for U.S. President Barack Obama and first lady Michelle Obama at the White House for Christmas in Washington, which was broadcast on December 20, 2009, on U.S. television broadcaster TNT.^[37] Bieber was also one of the performers at Dick Clark's New Year's Rockin' Eve with Ryan Seacrest on December 31, 2009.^[38] Bieber was a presenter at the 52nd Grammy Awards on January 31, 2010. He was invited to be a vocalist for the remake of We Are The World (a song written by Michael Jackson and Lionel Richie) for its 25th anniversary to benefit Haiti after the earthquake. Bieber sings the opening line, which was sung by Lionel Richie in the original version.^[39] On March 12, 2010, a version of K'naan's "Wavin' Flag" recorded by a collective of Canadian musicians known as Young Artists for Haiti was released. Bieber is featured in the song, performing the closing lines.

[edit] 2010–11: My World 2.0 and Never Say Never film

"Baby", the lead single from his debut album, My World 2.0, which features Ludacris, was released in January 2010 and became his biggest hit thus far, charting at number five in the U.S. and reaching the top ten in seven other countries.^[28] Two promo singles "Never Let You Go", and "U Smile" were top thirty hits on the U.S. Hot 100, and top twenty hits in Canada.^[28] According to review aggregator Metacritic, the album has received "generally favorable reviews".^[40] It debuted at number one on the U.S. Billboard 200, making Bieber the youngest solo male act to top the chart since Stevie Wonder in 1963.^[41] My World 2.0 also debuted at number one on the Canadian Albums Chart, Irish Albums Chart, Australian Albums Chart, and the New Zealand Albums Chart^[28] and reached the top ten of fifteen other countries.^[42][43] To promote the album, Bieber appeared on several live programs including The View, the 2010 Kids Choice Awards, Nightline, The Late Show with David Letterman, The Dome and 106 and Park.^[44] Bieber collaborated with Sean Kingston on his single "Eenie Meenie" which also appeared on Bieber's debut album. The song reached the top ten in the United Kingdom and Australia, and the top-twenty of most other markets.

Bieber performing at the Conseco Fieldhouse, in August 2010

On April 10, 2010, Bieber was the musical guest on Saturday Night Live.^[45] On July 4, 2010, Bieber performed at the Macy's Fourth of July Fireworks Spectacular in New York City.^[46] The second single from My World 2.0, "Somebody to Love", was released in April 2010, and a remix was released featuring Bieber's mentor Usher. The single reached number ten in Canada, number fifteen in the United States, and the top twenty in multiple international countries.

On June 23, 2010, Bieber went on his first official headlining tour, the My World Tour, starting in Hartford, Connecticut, to promote My World and My World 2.0.^[47] In July 2010, it was reported that Bieber was the most searched for celebrity on the Internet.^[48] That same month his music video, "Baby", surpassed Lady Gaga's "Bad Romance" to become the most viewed, and most disliked YouTube video ever.^[49] In September 2010, it was reported that Bieber accounted for three percent of all traffic on Twitter, according to an employee of the social-networking site.^[50]

Bieber began recording his second album in July 2010 in New York City.^[51] At this point, because of puberty, his voice was deeper than it was when he recorded his first album. In April 2010, the singer discussing his vocals remarked, "It cracks. Like every teenage boy, I'm dealing with it and I have the best vocal coach in the world. [...] Some of the notes I hit on "Baby" I can't hit anymore. We have to lower the key when I sing live."^[52]

Bieber performing in Jakarta during his My World Tour.

Bieber guest-starred in the season premiere of the CBS crime drama CSI: Crime Scene Investigation, which aired on September 23, 2010. He played a "troubled teen who is faced with a difficult decision regarding his only brother", who is also a serial bomber. Bieber was also in a subsequent episode which aired on February 17, 2011, in which his character is killed.^[53] Bieber performed a medley of "U Smile", "Baby", and "Somebody to Love" and briefly played the drums at the 2010 MTV Video Music Awards on September 12, 2010.^[54] Bieber announced in October 2010 that he would release an acoustic album, called My Worlds Acoustic.^[55] It was released on Black Friday in the United States and featured acoustic versions of songs from his previous albums, and accompanied the release of a completely new song titled "Pray".^[56]

A 3-D part-biopic, part-concert film starring Bieber entitled Justin Bieber: Never Say Never, was released on February 11, 2011, directed by Step Up 3D director Jon Chu. It topped the box office with an estimated gross of $12.4 million on its opening day from 3,105 theaters.^[57] It grossed $30.3 million for the weekend and was narrowly beaten by the romantic comedy Just Go With It, which grossed $31 million.^[58] Never Say Never is said to have exceeded industry expectations, nearly matching the $31.1 million grossed by Miley Cyrus's 2008 3-D concert film, Hannah Montana & Miley Cyrus: Best of Both Worlds Concert, which holds the record for the top debut for a music-documentary.^[59][60] Never Say Never grossed a total of $98,441,954 worldwide.^[61] The film is accompanied by his second remix album, Never Say Never – The Remixes, released February 14, 2011, and features remixes of songs from his debut album, with guest appearances from Miley Cyrus, Chris Brown, and Kanye West, among others.^[62]

[edit] 2011–present: Under The Mistletoe and Believe

On February 27, 2011, Bieber attended the 2011 Vanity Fair Oscar Party with American actress and singer Selena Gomez,^[63] confirming several months of media speculation about a romantic relationship between the pair.^{[64][65][66][67][68][69]}

In June 2011, Bieber was ranked number 2 on the Forbes list of Best-Paid Celebrities under 30. He is the youngest star and 1 of 7 musicians on the list raking in with $53 million earned in a 12 month period.^[70] On November 1, 2011, Bieber released Under the Mistletoe, his second studio album.^[71] It debuted at number one on the Billboard 200, selling 210,000 copies in its first week of release.^[72]

In late 2011, Bieber began recording his third studio album, entitled Believe. Kanye West and Drake are confirmed to be featured on the album.^[73] On February 22, 2012, Bieber announced via Twitter that the first single off Believe will be released in March 2012.^[74] The following week, Bieber appeared on The Ellen DeGeneres Show to announce that the first single will be called "Boyfriend" and was released on March 26, 2012.^[75] The song was co-written by Mike Posner.^[76] The second single, Die In Your Arms, was released on May 29th, 2012. ^[77]

Image[link]

Justin Bieber has a higher score on the Klout online "influence" scale than Barack Obama or The Dalai Lama.^[78] According to Jan Hoffman of The New York Times, part of Bieber's appeal stems from his YouTube channel. Long before he released his EP, My World, in mid-November, the YouTube videos attracted millions of views.^[18] Braun recognized the appeal. Prior to flying him to Atlanta, Braun wanted to "build him up more on YouTube first" and had Bieber record more home videos for the channel. "I said: 'Justin, sing like there’s no one in the room. But let's not use expensive cameras.' We'll give it to kids, let them do the work, so that they feel like it's theirs", recalled Braun.^[18] Bieber continues to upload videos to the same channel and has opened a Twitter account, from which he interacts with fans regularly;^[10] his account was reported in November 2010 to have over 6 million followers.^[79] Since then he has been consistently gaining followers at an average of 24,000 per day.^[80] The accounts also serve marketing purposes; for example, Bieber's music video for "One Time" only began selling quickly after it was uploaded to YouTube.^[81]

Bieber performing "Favorite Girl" in Zurich, Switzerland April 2011.

Usher comments that while he and Bieber were both signed at the same age, "I had the chance to ramp up my success, where this has happened to Bieber abruptly." As a result, Usher, Braun, Bieber's bodyguard Kenny, and other adults surrounding Bieber constantly coach him on handling fame and his public image.^[18] After signing Bieber, Usher appointed one of his former assistants, Ryan Good, to be Bieber's road manager and stylist. Good, once nicknamed Bieber's "swagger coach", created a "streetwise look" for the singer which consisted of baseball caps, hoodies, dog chains and flashy sneakers. Amy Kaufman of The Los Angeles Times comments, "Though a product of a middle-class suburban upbringing in Stratford, Ontario, Bieber's manner of dress and speech ("Wassup man, how you doin'?" or "It's like, you know, whateva' ") suggest he's mimicking his favorite rappers."^[82]

Bieber is often featured in teen magazines such as Tiger Beat,^[18] and has been labeled as a "teen heartthrob".^[83] Bieber has released a collection of nail varnishes to raise awareness for charity.^[84] Wax statues of Bieber are on display at Madame Tussauds wax museums in New York, Amsterdam and London.^[85] His change of hairstyle in 2010, and the consequent alterations to Bieber products, led to it being called 'the most expensive musical haircut of all time;^[86] one company spent $100,000 to fix its dolls for the 2011 Christmas season.^[87]

Bieber has been criticized for looking and sounding younger than his age, his teen-pop music, image, and frequent media attention.^[88] He has been a frequent target of Internet bloggers and message board posters, notably by users of Internet message board 4chan and users of YouTube.^[89] Nick Collins of The Daily Telegraph speculated that "Bieber's character also appears to strike a particularly sour note with his Internet critics, with many remarks commenting on his youthful appearance, his teen-pop songs, his image as a heart-throb to young teenage girls and his manner of speech".^[90]

Personal views and life[link]

Bieber is a Christian,^[91] and said he has a relationship with Jesus, talks to him and that "he's the reason I'm here".^[92]

Bieber's comments in a February 2011 profile in Rolling Stone sparked controversy.^[93] Asked about abstinence, Bieber responded, "I don't think you should have sex with anyone unless you love them." He said he does not "believe in abortion" and that it is "like killing a baby".^[94] He described sexual orientation as "everyone's own decision."^[95] Bieber has contributed to the It Gets Better Project,^[96] which aims to prevent suicide among LGBT youth.^[97]

Bieber has said he is not interested in obtaining United States citizenship and has criticized America's health care system. Praising Canada as being "the best country in the world", he cited its health care system as a model example.^[94]

In May 2012, Bieber purchased a 10,000 square-foot mansion on 1.3 acres of land, located in the community of Calabasas, California, a suburb of Los Angeles.^[98]

Twitter[link]

As of April 2012^[update], Bieber's Twitter account (@justinbieber) is the second most popular celebrity account behind that of Lady Gaga.^[99] By mid-April 2012, he had over 20 million followers.^[100][101] His follower acquisition is one new follower every other second.^[102][103] His popularity on Twitter at one point accounted for three percent of all Twitter related traffic, with a Twitter employee commenting that "racks of servers are dedicated" to Bieber.^{[103][104][105][106][107][108][109][110][111][112]} This resulted in over 180 million page views for the service each month.^[105] Bieber was frequently a trending topic on Twitter when the feature first launched^[105] because his fans frequently discussed him on the network. ^[113] and was named the top trending star on Twitter in 2010;^[114] Klout gave his account a score of 100.^[115][116]

The size of Bieber's and Gaga's follower bases are cited as a reason why marketers should pay attention to Twitter:^[117] with an ability to reach millions of people with a single tweet.^[117] 8.3% of tweets mentioning "bieber" were semi-automated and probably Twitter related spam.^[118] Research done about Twitter and the 2011 Egyptian revolution includes Bieber as he made tweets about the topic at a time when he had roughly 8 million followers. His multiple tweets resulted in 32,000 responses each, which made Bieber's Twitter account one of the single largest nodes for discussion about the uprising one of the largest on Twitter.^[119][120]

In March 2012, Bieber fans launched an unsuccessful attempt to unseat Lady Gaga as the most popular celebrity on Twitter. Neither Bieber nor Lady Gaga discussed their mutual fanbase's campaigns on Twitter.^[121]

Discography[link]

Justin Bieber portal

• My World 2.0 (2010)
• Under the Mistletoe (2011)
• Believe (2012)

Tours[link]

• 2009: Urban Behavior Tour
• 2010–2011: My World Tour
• 2012-2013: Believe Tour

Filmography[link]

Awards and nominations[link]

References[link]

Further reading[link]

External links[link]

Wikimedia Commons has media related to: Justin Bieber

Wikiquote has a collection of quotations related to: Justin Bieber

• Official website
• Justin Bieber at the Internet Movie Database
• Justin Bieber at the Open Directory Project
• Justin Bieber on Twitter