A symbol of the set of real numbers (ℝ)

Real numbers can be thought of as points on an infinitely long number line.

In mathematics, a real number is a value that represents a quantity along a continuous line. The real numbers include all the rational numbers, such as the integer −5 and the fraction 4/3, and all the irrational numbers such as √2 (1.41421356... the square root of two, an irrational algebraic number) and π (3.14159265..., a transcendental number). Real numbers can be thought of as points on an infinitely long line called the number line or real line, where the points corresponding to integers are equally spaced. Any real number can be determined by a possibly infinite decimal representation such as that of 8.632, where each consecutive digit is measured in units one tenth the size of the previous one. The real line can be thought of as a part of the complex plane, and correspondingly, complex numbers include real numbers as a special case.

These descriptions of the real numbers are not sufficiently rigorous by the modern standards of pure mathematics. The discovery of a suitably rigorous definition of the real numbers — indeed, the realization that a better definition was needed — was one of the most important developments of 19th century mathematics. The currently standard axiomatic definition is that real numbers form the unique complete totally ordered field (R,+,·,<), up to isomorphism,^[1] Whereas popular constructive definitions of real numbers include declaring them as equivalence classes of Cauchy sequences of rational numbers, Dedekind cuts, or certain infinite "decimal representations", together with precise interpretations for the arithmetic operations and the order relation. These definitions are equivalent in the realm of classical mathematics.

Basic properties[link]

A real number may be either rational or irrational; either algebraic or transcendental; and either positive, negative, or zero. Real numbers are used to measure continuous quantities. They may in theory be expressed by decimal representations that have an infinite sequence of digits to the right of the decimal point; these are often represented in the same form as 324.823122147… The ellipsis (three dots) indicate that there would still be more digits to come.

More formally, real numbers have the two basic properties of being an ordered field, and having the least upper bound property. The first says that real numbers comprise a field, with addition and multiplication as well as division by nonzero numbers, which can be totally ordered on a number line in a way compatible with addition and multiplication. The second says that if a nonempty set of real numbers has an upper bound, then it has a least upper bound. The second condition distinguishes the real numbers from the rational numbers: for example, the set of rational numbers whose square is less than 2 is a set with an upper bound (e.g. 1.5) but no least upper bound: hence the rational numbers do not satisfy the least upper bound property.

In physics[link]

In the physical sciences, most physical constants such as the universal gravitational constant, and physical variables, such as position, mass, speed, and electric charge, are modeled using real numbers. In fact, the fundamental physical theories such as classical mechanics, electromagnetism, quantum mechanics, general relativity and the standard model are described using mathematical structures, typically smooth manifolds or Hilbert spaces, that are based on the real numbers although actual measurements of physical quantities are of finite accuracy and precision.

In some recent developments of theoretical physics stemming from the holographic principle, the Universe is seen fundamentally as an information store, essentially zeroes and ones, organized in much less geometrical fashion and manifesting itself as space-time and particle fields only on a more superficial level. This approach removes the real number system from its foundational role in physics and even prohibits the existence of infinite precision real numbers in the physical universe by considerations based on the Bekenstein bound.^[2]

In computation[link]

Computer arithmetic cannot directly operate on real numbers, but only on a finite subset of rational numbers, limited by the number of bits used to store them, whether as floating-point numbers or arbitrary precision numbers. However, computer algebra systems can operate on irrational quantities exactly by manipulating formulas for them (such as Failed to parse (Missing texvc executable; please see math/README to configure.): \textstyle\sqrt 2 , Failed to parse (Missing texvc executable; please see math/README to configure.): \textstyle\arcsin \left({{2}\over{23}}\right) , orFailed to parse (Missing texvc executable; please see math/README to configure.): \textstyle\int_{0}^{1} {x^{x}}\;dx ) rather than their rational or decimal approximation;^[3] however, it is not in general possible to determine whether two such expressions are equal (the Constant problem).

A real number is called computable if there exists an algorithm that yields its digits. Because there are only countably many algorithms,^[4] but an uncountable number of reals, almost all real numbers fail to be computable. Moreover, the equality of two computable numbers is an undecidable problem. Some constructivists accept the existence of only those reals that are computable. The set of definable numbers is broader, but still only countable.

Notation[link]

Mathematicians use the symbol R (or alternatively, Failed to parse (Missing texvc executable; please see math/README to configure.): \mathbb{R} , the letter "R" in blackboard bold, Unicode ℝ – U+211D) to represent the set of all real numbers (as this set is naturally endowed with a structure of field, the expression field of the real numbers is more frequently used than set of all real numbers). The notation Rⁿ refers to the Cartesian product of n copies of R, which is an n-dimensional vector space over the field of the real numbers; this vector space may be identified to the n-dimensional space of Euclidean geometry as soon as a coordinate system has been chosen in the latter. For example, a value from R³ consists of three real numbers and specifies the coordinates of a point in 3-dimensional space.

In mathematics, real is used as an adjective, meaning that the underlying field is the field of the real numbers (or the real field). For example real matrix, real polynomial and real Lie algebra. As a substantive, the term is used almost strictly in reference to the real numbers themselves (e.g., The "set of all reals").

History[link]

Vulgar fractions had been used by the Egyptians around 1000 BC; the Vedic "Sulba Sutras" ("The rules of chords") in, ca. 600 BC, include what may be the first 'use' of irrational numbers. The concept of irrationality was implicitly accepted by early Indian mathematicians since Manava (c. 750–690 BC), who were aware that the square roots of certain numbers such as 2 and 61 could not be exactly determined.^{[5][verification needed]} Around 500 BC, the Greek mathematicians led by Pythagoras realized the need for irrational numbers, in particular the irrationality of the square root of 2.

The Middle Ages brought the acceptance of zero, negative, integral, and fractional numbers, first by Indian and Chinese mathematicians, and then by Arabic mathematicians, who were also the first to treat irrational numbers as algebraic objects,^[6] which was made possible by the development of algebra. Arabic mathematicians merged the concepts of "number" and "magnitude" into a more general idea of real numbers.^[7] The Egyptian mathematician Abū Kāmil Shujā ibn Aslam (c. 850–930) was the first to accept irrational numbers as solutions to quadratic equations or as coefficients in an equation, often in the form of square roots, cube roots and fourth roots.^{[8][verification needed]}

In the 16th century, Simon Stevin created the basis for modern decimal notation, and insisted that there is no difference between rational and irrational numbers in this regard.

In the 17th century, Descartes introduced the term "real" to describe roots of a polynomial, distinguishing them from "imaginary" ones.

In the 18th and 19th centuries there was much work on irrational and transcendental numbers. Johann Heinrich Lambert (1761) gave the first flawed proof that π cannot be rational;^{[citation needed]} Adrien-Marie Legendre (1794) completed the proof, and showed that π is not the square root of a rational number. Paolo Ruffini (1799) and Niels Henrik Abel (1842) both constructed proofs of Abel–Ruffini theorem: that the general quintic or higher equations cannot be solved by a general formula involving only arithmetical operations and roots.

Évariste Galois (1832) developed techniques for determining whether a given equation could be solved by radicals, which gave rise to the field of Galois theory. Joseph Liouville (1840) showed that neither e nor e² can be a root of an integer quadratic equation, and then established existence of transcendental numbers, the proof being subsequently displaced by Georg Cantor (1873). Charles Hermite (1873) first proved that e is transcendental, and Ferdinand von Lindemann (1882), showed that π is transcendental. Lindemann's proof was much simplified by Weierstrass (1885), still further by David Hilbert (1893), and has finally been made elementary by Adolf Hurwitz and Paul Gordan.

The development of calculus in the 18th century used the entire set of real numbers without having defined them cleanly. The first rigorous definition was given by Georg Cantor in 1871. In 1874 he showed that the set of all real numbers is uncountably infinite but the set of all algebraic numbers is countably infinite. Contrary to widely held beliefs, his first method was not his famous diagonal argument, which he published in 1891. See Cantor's first uncountability proof.

Definition[link]

The real number system Failed to parse (Missing texvc executable; please see math/README to configure.): (\mathbb R,+,\cdot,<)

can be defined axiomatically up to an isomorphism, which is described below. There are also many ways to construct "the" real number system, for example, starting from natural numbers, then defining rational numbers algebraically, and finally defining real numbers as equivalence classes of their Cauchy sequences or as Dedekind cuts, which are certain subsets of rational numbers. Another possibility is to start from some rigorous axiomatization of Euclidean geometry (Hilbert, Tarski etc.) and then define the real number system geometrically. From the structuralist point of view all these constructions are on equal footing.

Axiomatic approach[link]

Let R denote the set of all real numbers. Then:

• The set R is a field, meaning that addition and multiplication are defined and have the usual properties.
• The field R is ordered, meaning that there is a total order ≥ such that, for all real numbers x, y and z:
  • if x ≥ y then x + z ≥ y + z;
  • if x ≥ 0 and y ≥ 0 then xy ≥ 0.
• The order is Dedekind-complete; that is, every non-empty subset S of R with an upper bound in R has a least upper bound (also called supremum) in R.

The last property is what differentiates the reals from the rationals. For example, the set of rationals with square less than 2 has a rational upper bound (e.g., 1.5) but no rational least upper bound, because the square root of 2 is not rational.

The real numbers are uniquely specified by the above properties. More precisely, given any two Dedekind-complete ordered fields R₁ and R₂, there exists a unique field isomorphism from R₁ to R₂, allowing us to think of them as essentially the same mathematical object.

For another axiomatization of R, see Tarski's axiomatization of the reals.

Construction from the rational numbers[link]

The real numbers can be constructed as a completion of the rational numbers in such a way that a sequence defined by a decimal or binary expansion like (3, 3.1, 3.14, 3.141, 3.1415,...) converges to a unique real number. For details and other constructions of real numbers, see construction of the real numbers.

Properties[link]

Completeness[link]

A main reason for using real numbers is that the reals contain all limits. More precisely, every sequence of real numbers having the property that consecutive terms of the sequence become arbitrarily close to each other necessarily has the property that after some term in the sequence the remaining terms are arbitrarily close to some specific real number. In mathematical terminology, this means that the reals are complete (in the sense of metric spaces or uniform spaces, which is a different sense than the Dedekind completeness of the order in the previous section). This is formally defined in the following way:

A sequence (x_n) of real numbers is called a Cauchy sequence if for any ε > 0 there exists an integer N (possibly depending on ε) such that the distance |x_n − x_m| is less than ε for all n and m that are both greater than N. In other words, a sequence is a Cauchy sequence if its elements x_n eventually come and remain arbitrarily close to each other.

A sequence (x_n) converges to the limit x if for any ε > 0 there exists an integer N (possibly depending on ε) such that the distance |x_n − x| is less than ε provided that n is greater than N. In other words, a sequence has limit x if its elements eventually come and remain arbitrarily close to x.

Notice that every convergent sequence is a Cauchy sequence. The converse is also true:

Every Cauchy sequence of real numbers is convergent to a real number.

That is, the reals are complete.

Note that the rationals are not complete. For example, the sequence (1, 1.4, 1.41, 1.414, 1.4142, 1.41421, ...), where each term adds a digit of the decimal expansion of the positive square root of 2, is Cauchy but it does not converge to a rational number. (In the real numbers, in contrast, it converges to the positive square root of 2.)

The existence of limits of Cauchy sequences is what makes calculus work and is of great practical use. The standard numerical test to determine if a sequence has a limit is to test if it is a Cauchy sequence, as the limit is typically not known in advance.

For example, the standard series of the exponential function

Failed to parse (Missing texvc executable; please see math/README to configure.): \mathrm{e}^x = \sum_{n=0}^{\infty} \frac{x^n}{n!}

converges to a real number because for every x the sums

Failed to parse (Missing texvc executable; please see math/README to configure.): \sum_{n=N}^{M} \frac{x^n}{n!}

can be made arbitrarily small by choosing N sufficiently large. This proves that the sequence is Cauchy, so we know that the sequence converges even if the limit is not known in advance.

"The complete ordered field"[link]

The real numbers are often described as "the complete ordered field", a phrase that can be interpreted in several ways.

First, an order can be lattice-complete. It is easy to see that no ordered field can be lattice-complete, because it can have no largest element (given any element z, z + 1 is larger), so this is not the sense that is meant.

Additionally, an order can be Dedekind-complete, as defined in the section Axioms. The uniqueness result at the end of that section justifies using the word "the" in the phrase "complete ordered field" when this is the sense of "complete" that is meant. This sense of completeness is most closely related to the construction of the reals from Dedekind cuts, since that construction starts from an ordered field (the rationals) and then forms the Dedekind-completion of it in a standard way.

These two notions of completeness ignore the field structure. However, an ordered group (in this case, the additive group of the field) defines a uniform structure, and uniform structures have a notion of completeness (topology); the description in the section Completeness above is a special case. (We refer to the notion of completeness in uniform spaces rather than the related and better known notion for metric spaces, since the definition of metric space relies on already having a characterisation of the real numbers.) It is not true that R is the only uniformly complete ordered field, but it is the only uniformly complete Archimedean field, and indeed one often hears the phrase "complete Archimedean field" instead of "complete ordered field". Since it can be proved that any uniformly complete Archimedean field must also be Dedekind-complete (and vice versa, of course), this justifies using "the" in the phrase "the complete Archimedean field". This sense of completeness is most closely related to the construction of the reals from Cauchy sequences (the construction carried out in full in this article), since it starts with an Archimedean field (the rationals) and forms the uniform completion of it in a standard way.

But the original use of the phrase "complete Archimedean field" was by David Hilbert, who meant still something else by it. He meant that the real numbers form the largest Archimedean field in the sense that every other Archimedean field is a subfield of R. Thus R is "complete" in the sense that nothing further can be added to it without making it no longer an Archimedean field. This sense of completeness is most closely related to the construction of the reals from surreal numbers, since that construction starts with a proper class that contains every ordered field (the surreals) and then selects from it the largest Archimedean subfield.

Advanced properties[link]

The reals are uncountable, that is, there are strictly more real numbers than natural numbers, even though both sets are infinite. In fact, the cardinality of the reals equals that of the set of subsets (i.e., the power set) of the natural numbers, and Cantor's diagonal argument states that the latter set's cardinality is strictly bigger than the cardinality of N. Since only a countable set of real numbers can be algebraic, almost all real numbers are transcendental. The non-existence of a subset of the reals with cardinality strictly between that of the integers and the reals is known as the continuum hypothesis. The continuum hypothesis can neither be proved nor be disproved; it is independent from the axioms of set theory.

As a topological space, the real numbers are separable. This is because the set of rationals, which is countable, is dense in the real numbers. The irrational numbers are also dense in the real numbers, however they are uncountable and have the same cardinality as the reals.

The real numbers form a metric space: the distance between x and y is defined as the absolute value |x − y|. By virtue of being a totally ordered set, they also carry an order topology; the topology arising from the metric and the one arising from the order are identical, but yield different presentations for the topology – in the order topology as intervals, in the metric topology as epsilon-balls. The Dedekind cuts construction uses the order topology presentation, while the Cauchy sequences construction uses the metric topology presentation. The reals are a contractible (hence connected and simply connected), separable and complete metric space of Hausdorff dimension 1. The real numbers are locally compact but not compact. There are various properties that uniquely specify them; for instance, all unbounded, connected, and separable order topologies are necessarily homeomorphic to the reals.

Every nonnegative real number has a square root in R, although no negative number does. This shows that the order on R is determined by its algebraic structure. Also, every polynomial of odd degree admits at least one real root: these two properties make R the premier example of a real closed field. Proving this is the first half of one proof of the fundamental theorem of algebra.

The reals carry a canonical measure, the Lebesgue measure, which is the Haar measure on their structure as a topological group normalised such that the unit interval [0,1] has measure 1.

The supremum axiom of the reals refers to subsets of the reals and is therefore a second-order logical statement. It is not possible to characterize the reals with first-order logic alone: the Löwenheim–Skolem theorem implies that there exists a countable dense subset of the real numbers satisfying exactly the same sentences in first order logic as the real numbers themselves. The set of hyperreal numbers satisfies the same first order sentences as R. Ordered fields that satisfy the same first-order sentences as R are called nonstandard models of R. This is what makes nonstandard analysis work; by proving a first-order statement in some nonstandard model (which may be easier than proving it in R), we know that the same statement must also be true of R.

Generalizations and extensions[link]

The real numbers can be generalized and extended in several different directions:

• The complex numbers contain solutions to all polynomial equations and hence are an algebraically closed field unlike the real numbers. However, the complex numbers are not an ordered field.
• The affinely extended real number system adds two elements +∞ and −∞. It is a compact space. It is no longer a field, not even an additive group, but it still has a total order; moreover, it is a complete lattice.
• The real projective line adds only one value ∞. It is also a compact space. Again, it is no longer a field, not even an additive group. However, it allows division of a non-zero element by zero. It is not ordered anymore.
• The long real line pastes together ℵ₁* + ℵ₁ copies of the real line plus a single point (here ℵ₁* denotes the reversed ordering of ℵ₁) to create an ordered set that is "locally" identical to the real numbers, but somehow longer; for instance, there is an order-preserving embedding of ℵ₁ in the long real line but not in the real numbers. The long real line is the largest ordered set that is complete and locally Archimedean. As with the previous two examples, this set is no longer a field or additive group.
• Ordered fields extending the reals are the hyperreal numbers and the surreal numbers; both of them contain infinitesimal and infinitely large numbers and thus are not Archimedean.
• Self-adjoint operators on a Hilbert space (for example, self-adjoint square complex matrices) generalize the reals in many respects: they can be ordered (though not totally ordered), they are complete, all their eigenvalues are real and they form a real associative algebra. Positive-definite operators correspond to the positive reals and normal operators correspond to the complex numbers.

"Reals" in set theory[link]

In set theory, specifically descriptive set theory, the Baire space is used as a surrogate for the real numbers since the latter have some topological properties (connectedness) that are a technical inconvenience. Elements of Baire space are referred to as "reals".

Real numbers and logic[link]

The real numbers are most often formalized using the Zermelo-Fraenkel axiomatization of set theory, but some mathematicians study the real numbers with other logical foundations of mathematics. In particular, the real numbers are also studied in reverse mathematics and in constructive mathematics.^[9]

Abraham Robinson's theory of nonstandard or hyperreal numbers extends the set of the real numbers by infinitesimal numbers, which allows building infinitesimal calculus in a way closer to the usual intuition of the notion of limit. Edward Nelson's internal set theory is a non-Zermelo-Fraenkel set theory that considers non-standard real numbers as elements of the set of the reals (and not of an extension of it, as in Robinson's theory).

The continuum hypothesis posits that the cardinality of the set of the real numbers is Failed to parse (Missing texvc executable; please see math/README to configure.): \aleph_1 , i.e. the smallest infinite cardinal number after Failed to parse (Missing texvc executable; please see math/README to configure.): \aleph_0 , the cardinality of the integers. Paul Cohen proved in 1963 that it is an axiom independent of the other axioms of set theory; that is, one may choose either the continuum hypothesis or its negation as an axiom of set theory, without contradiction.

See also[link]

Notes[link]

References[link]

• Georg Cantor, 1874, "Über eine Eigenschaft des Inbegriffes aller reellen algebraischen Zahlen", Journal für die Reine und Angewandte Mathematik, volume 77, pages 258–262.
• Robert Katz, 1964, Axiomatic Analysis, D. C. Heath and Company.
• Edmund Landau, 2001, ISBN 0-8218-2693-X, Foundations of Analysis, American Mathematical Society.
• Howie, John M., Real Analysis, Springer, 2005, ISBN 1-85233-314-6

External links[link]

• The real numbers: Pythagoras to Stevin
• The real numbers: Stevin to Hilbert
• The real numbers: Attempts to understand
• What are the "real numbers," really?

Selena Gomez
Gomez attending "The 6th Annual Hollywood Style Awards", Beverly Hills, CA on Oct. 10, 2009
Background information
Birth name	Selena Marie Gomez
Born	(1992-07-22) July 22, 1992 (age 19) Grand Prairie, Texas, U.S.
Genres	Pop, dance, pop rock[1]
Occupations	Actress, singer, Fashion Designer
Instruments	Vocals, piano, guitar, drums
Years active	2002–present
Labels	Hollywood
Associated acts	Selena Gomez & the Scene, Demi Lovato, Taylor Swift
Website	SelenaGomez.com

Selena Marie Gomez (born July 22, 1992)^[2] is an American actress and singer best known for portraying Alex Russo in the Emmy Award-winning Disney Channel television series Wizards of Waverly Place. She subsequently ventured into feature films and has starred in the television movies Another Cinderella Story, Wizards of Waverly Place: The Movie, and Princess Protection Program. She made her starring theatrical film debut in Ramona and Beezus.

Her career has expanded into the music industry; Gomez is the lead singer and founder of the pop band Selena Gomez & the Scene, which has released three RIAA Gold certified studio albums, Kiss & Tell, A Year Without Rain, and When the Sun Goes Down, spawned three RIAA Platinum certified singles, "Naturally", "Who Says" and "Love You Like a Love Song" and charted four No. 1 Billboard Hot Dance Club Songs.^[3] Gomez has also contributed to the soundtracks of Tinker Bell, Another Cinderella Story, Wizards of Waverly Place, and Shake It Up after signing a record deal with Hollywood Records.

In 2008, Gomez was designated a UNICEF Goodwill Ambassador.^[4]

Early life[link]

Gomez was born in Grand Prairie, Texas.^[2] She is the daughter of former stage actress Amanda Dawn "Mandy" Teefey (née Cornett) and Ricardo Joel Gomez.^[5][6][7] Her father is of Mexican ancestry, and her mother is of part Italian descent.^[8][9] Regarding her Hispanic heritage, Gomez said: "My family does have Quinceañeras, and we go to the communion church. We do everything that's Catholic, but we don't really have anything traditional except [that we] go to the park and have barbecues on Sundays after church."^[10] Her birth parents divorced when she was five years old, and she was raised as an only child by her working mother.^[5][11] In 2006, Mandy remarried Brian Teefey.^[12] She was named after Tejano singer Selena, who died almost three years after Gomez was born.^[13] In a 2009 interview with People, Gomez mentioned that she developed an early interest in acting from watching her mother prepare for and act in theater productions.^[11] She earned a high school diploma through homeschooling in May 2010.^[14]

Career[link]

[edit] 2002–06: Barney & Friends and early work

Gomez began her acting career at age seven, playing Gianna on Barney & Friends.^[15] She later had minor roles in Spy Kids 3-D: Game Over and the TV film Walker, Texas Ranger: Trial By Fire. Gomez also starred in the television movie Brain Zapped. (Selena Gomez also found out that she wanted to be an actress because in E Special she states that "I would also watch my mom on stage do her lines".)

In 2004, Gomez was discovered by the Disney Channel in a USA-wide scouting.^[16] Gomez appeared as a guest star on The Suite Life of Zack & Cody and had a guest appearance – that later turned into a recurring role – on Hannah Montana from seasons two to three. Gomez previously taped two different pilots that were spin-offs to two previous Disney series.^[17] The first one, What's Stevie Thinking?, was the spin-off to Lizzie McGuire. Gomez played Stevie Sanchez, Miranda Sanchez's little sister. The other show was titled Arwin!, the spin-off to The Suite Life of Zack & Cody, in which she played Alexa. Neither series was picked up.

[edit] 2007–09: Wizards of Waverly Place and Selena Gomez & The Scene

Gomez on the studio set of Wizards of Waverly Place before filming an episode for the show's first season in April 2007

In early 2007 Gomez was cast in the Disney Channel series Wizards of Waverly Place as one of the three main characters, Alex Russo. The show premiered to an audience of 5.9 million, becoming a hit. Many news outlets began dubbing Gomez the next 'Miley Cyrus' causing some controversy and a reported 'feud'. Gomez clarified that there was no feud and that she was flattered by the comparison, saying: "It's a little overwhelming, but I think really, it's a compliment. She's obviously extremely successful, and I think she's a wonderful performer ... So being compared to her, I was very, very flattered."^[18] Gomez recorded four songs, one of which was a cover, for theWizards of Waverly Place soundtrack, only one single (Magic) from the album was released.

In 2008, Gomez recorded a cover of "Cruella de Vil"—which included a music video—for the compilation albumDisneyMania 6. Gomez also recorded "Fly to Your Heart" for the 2008 animated film Tinker Bell. In July 2008, before Gomez' sixteenth birthday, she signed a recording deal with Hollywood Records, a music label owned by Disney.^[19] In May, of the same year, Gomez was featured, with Forever the Sickest Kids, on a duet version of the non-album song "Whoa Oh!".^[20] The same year Gomez appeared in Another Cinderella Story, the direct-to-DVD sequel to the 2004 Hilary Duff film, opposite Drew Seeley. She also had a minor voiceover role as one the Mayor's ninety-six daughters in Horton Hears a Who! which released in March of that year. In April, Lacey Rose, of Forbes ranked Gomez as being fifth on their "Eight Hot Kid Stars To Watch" list; and Rose described Gomez as having been "a multitalented teen".^[21] Gomez recorded three songs for the movie's soundtrack.

In 2009, Gomez formed the teen pop band Selena Gomez & the Scene. Kiss & Tell, the band's debut studio album and was released on September 29, 2009 by Hollywood Records. On March 5, 2010, the album was certified Gold by RIAA.^[3] The album's single, "Naturally", was certified Platinum by the RIAA on July 15, 2010.^[3] In February 2009, Gomez signed on to star as one of the two female leads in Ramona and Beezus, a film adaption of the children's novel series by Beverly Cleary.^[22][23] Gomez stated that she felt no pressure in taking more adult roles: "I think I’m fully aware of my audience and I’m still just a kid myself. I wouldn’t do a role I don’t feel comfortable doing or that my audience wouldn’t feel comfortable seeing."^[24]

In June 2009, Gomez did a guest appearance as herself in one episode of best friend Demi Lovato's Disney Channel television show, Sonny with a Chance, entitled "Battle of The Network Stars". That same month Gomez appeared alongside Lovato in the made-for-television Disney Channel movie, Princess Protection Program.^[25] The telecast garnered 8.5 million viewers becoming, at the time, the third most watched Disney Channel Original Movie.^[26] One month later, Gomez, along with two cast members of Wizards of Waverly Place appeared in a television three-way cross-over episode with Hannah Montana and The Suite Life on Deck, entitled Wizards on Deck with Hannah Montana.

On August 28, 2009 two months after appearing in Princess Protection Program, Gomez starred in Wizards of Waverly Place: The Movie, a made-for-television film based on the show.^[27] The film premiered to an audience of 11.4 million viewers becoming cable's No. 1 scripted telecast of 2009 and Disney Channel's second most-viewed film premiere after High School Musical 2.^[28] In September 2009, Wizards of Waverly Place won "Outstanding Children's Program" at the 61st Primetime Emmy Awards.^[29] In 2010, the film adaptation won the series its second consecutive Emmy for "Outstanding Children's Program" at the 62nd Primetime Emmy Awards.^[29]

[edit] 2010–2011:Theatrical film debut, A Year Without Rain and When The Sun Goes Down

Gomez on location in Paris, France filming Monte Carlo in June 2010

Gomez's first theatrical film Ramona & Beezus premiered on July 23, 2010 and met with generally positive reviews.^[30] In March 2010, Variety reported that Gomez was set to star as one of the three lead roles in Monte Carlo, alongside Leighton Meester and Katie Cassidy.^[31] In the film Gomez plays Grace, a girl who’s “mistaken for a socialite while on a trip to Paris.”^[32] To prepare for the role Gomez learned how to play polo and also took two weeks of vocal training to learn two different British accents.^[33][34] The same year Gomez confirmed that the fourth season of her hit Disney Channel show, Wizards of Waverly Place, would be its last.

Gomez performing at the 2011 MuchMusic Video Awards.

On September 17, 2010 , Selena Gomez and The Scene released their second studio album, A Year Without Rain The record debuted on the Billboard 200 at number 4, selling 66,000 copies. On January 19, 2011, the album was certified Gold by RIAA.^[3] As of April 2011, the band has sold 1,354,000 albums in the United States.^[35] To support the album, the band embarked on the mini-tour A Year Without Rain Tour. In February 2011, Deadline.com reported that Universal Pictures and Strike Entertainment had acquired the novel Thirteen Reasons Why by Jay Asher with Gomez attached to the lead.^[36] That same month TV Guide reported that Gomez would make a cameo in the Muppets film.^[37] On March 23, 2011, Hollywood Records announced through a press release that Selena Gomez & The Scene would be embarking on their third concert tour in the United States, the We Own the Night Tour ran during the summer of 2011.^[38] Production for the final season of Wizards of Waverly Place came to a wrap on May 14, 2011.^[39] Gomez co-hosted the 2011 MuchMusic Video Awards on June 19.^[40] She also hosted the 2011 MTV EMAs on November 6, 2011, in Belfast, Northern Ireland, where she performed her band's single "Hit the Lights". Near the end of 2011, it was reported Gomez was in talks to star in two upcoming films. Deadline.com announced in October that Gomez would take part in the comedy Hot Mess.^[41]

In early November, Variety reported that Gomez was in talks to star in the upcoming film Spring Breakers alongside James Franco and Vanessa Hudgens.^[42] Gomez confirmed to MTV that she had signed on for the project and that production will begin in early 2012.^[43] On June 28, 2011, Selena Gomez & the scene released their third studio album, When the Sun Goes Down, previously titledOtherside,^[44] The album debuted at number 4 on the Billboard 200, selling 78,000 copies its first week and the following week, the album rose to number 3 on the Billboard chart, becoming the band's highest charting album to date.^[45][46] On November 17, 2011, the album was certified platinum.^[3] The album's lead single, "Who Says" was certified Platinum by RIAA on June 23, 2011 and has become the band's highest charting song on the Billboard Hot 100 to date, peaking at number 21.^[3][47] The second single, "Love You Like a Love Song", was certified Platinum by RIAA on December 2, 2011, and became the act's first to sell over two-million copies.^[3][48]

2012–present: Focus on film[link]

In January 2012, Gomez announced that she would put her music career on hold.^[49] This was later reaffirmed as Gomez wrote on her Facebook page that she was taking a break from music in order to focus on her acting career, "my band and I are going our separate ways for a while. This year is all about films and acting and I want my band to play music wherever with whoever. We will be back but, it will be a good while."^[50] In February 2012, Gomez announced that the band would be taking a hiatus, so that she could focus on film for the year. She encouraged her band mates to work with other artists during the hiatus.^[51] The same month, it was announced that Gomez will replace Miley Cyrus in the animated comedy Hotel Transylvania playing Mavis, the daughter of Dracula who will be voiced by Adam Sandler.^[52] As of March 2012, Gomez has been cast in four upcoming films; in which three of them she has been cast as a lead role. She will first appear in Hotel Transylvania, an animated film, voicing the character of Mavis, who was originally supposed to be voiced by Miley Cyrus, however Cyrus dropped out of the film in early 2012 in order to focus on her music career.^[53] The film is scheduled to be released on September 21, 2012.^[54] Next, Gomez will appear in Spring Breakers, which is currently being filmed on location in Sarasota, Florida. The film is being written and directed by Harmony Korine.^[55] Gomez has also been cast as the main role of Hannah Baker in the film adaptation of young-adult fiction novel, 13 Reasons Why. The novel was written by Jay Asher.^[56] She will also play the lead role in a film called Hot Mess, a comedy film directed by Dave Meyers.^[56] On April 7, 2012, Gomez posted a video for fans in which she revealed that she will be filming a new movie called "The Getaway" in Bulgaria. ^[57]

Other projects[link]

Philanthropy[link]

Selena Gomez performs at the KISS 108 Jingle Ball in December 2010

Gomez was involved in the UR Votes Count campaign which encouraged teenagers to learn more about 2008 presidential candidates Barack Obama and John McCain.^[58] In October 2008, Gomez participated in St. Jude's Children's Hospital "Runway For Life" benefit.^[59] Gomez is a spokesperson for Borden Milk; she is featured in the campaign's print and television ads.^[60] She is the ambassador of DoSomething.org after being involved with the charity Island Dog, which help dogs in Puerto Rico.^[61] She got involved while filming Wizards of Waverly Place: The Movie in Puerto Rico.^[62] Gomez is a spokesperson for State Farm Insurance, and is featured in their TV commercials; which air on the Disney Channel, to raise awareness of being a safe driver.^[63] Gomez is also involved with the charity RAISE Hope For Congo, an initiative of the Enough Project, which helps raise awareness about conflict minerals and violence against Congolese women.^[64]

In October 2008, Gomez was named UNICEF's spokesperson for the Trick-or-Treat for UNICEF campaign, which encouraged children to raise money on Halloween to help children around the world.^[4] She said that she was "extremely excited" to "encourage other kids to make a difference in the world."^[4]

In August 2009, a 17-year-old Gomez became the youngest UNICEF ambassador ever, passing fellow songstress Hayley Westenra, who was 18 when she was chosen. In her first official field mission, Gomez traveled to Ghana on September 4, 2009 for a week to witness first-hand the stark conditions of vulnerable children that lack vital necessities including clean water, nourishment, education and healthcare.^[65][66] Gomez explained during an interview with Associated Press that she wanted to use her star power to bring awareness to Ghana: “That’s why I feel very honored to have a voice that kids listen to and take into consideration [...] I had people on my tour asking me where IS Ghana, and they Googled it [...] and because I went there, they now know where Ghana is. So it’s pretty incredible.”^[66][67] Gomez said of her role as ambassador that: "Every day 25,000 children die from preventable causes. I stand with UNICEF in the belief that we can change that number from 25,000 to zero. I know we can achieve this because every moment, UNICEF is on the ground providing children with the lifesaving assistance needed to ensure zero becomes a reality."^[65]

Gomez was named spokesperson for UNICEF's 2009 Trick-or-Treat campaign, for the second year in a row.^[68] Gomez, who raised over $700,000 for the charity in 2008, stated that she hopes to be able to raise 1 million dollars in 2009.^[66] Gomez participated in a celebrity auction^[69] and hosted a live web cast series on Facebook in support of the Trick-or-Treat for UNICEF campaign.^[70] Gomez returned as the UNICEF spokesperson for the 60th anniversary of Trick-or-Treat for UNICEF campaign in 2010.^[71] In celebration of the 60th anniversary, Gomez and her band, The Scene, held a benefit concert donating all proceeds to the campaign.^[72]. On January 22nd 2010, Gomez participated in the Hope for Haiti Now Telethon with a number of other celebrities^[73].

In February 2011, Gomez traveled to Chile to witness and meet with the families of UNICEF's supported program, "Programa Puente" which helps families better understand and develops skills to deal effectively with early childhood education, development and other issues related to raising children. From her field trip experience, Gomez said "UNICEF is helping Chilean families get out of poverty, prevent violence within the home and promote education. To witness first hand these families' struggles, and also their hope and perseverance, was truly inspiring."^[74] In March 2011, Gomez participated in the UNICEF Tap Project's "Celebrity Tap Pack," limited-edition, custom-made water bottles featuring tap water from the homes of each celebrity advocate, in order to raise funds and increase profile for the clean water and sanitation programs.^[75] She is also featured in videos promoting the campaign.^[76][77]

Gomez is involved in Disney's Friends for Change, an organization which promotes "environmently-friendly behavior", and appears in its public service announcements.^[78] Gomez, Demi Lovato, Miley Cyrus, and the Jonas Brothers recorded "Send It On", a charity single with all of its proceeds to the Disney Worldwide Conservation Fund.^[79][80] It debuted on the Billboard Hot 100 at number 20.^[79] Also in 2009, Gomez made a surprise visit to a Los Angeles elementary school as part of the "A Day Made Better" program that was sponsored by OfficeMax. During her visit, Gomez gave the school an award and $1,000 worth of school supplies, and talked to students about the importance of giving back to the community.^[81][82]

Gomez is also the owner of six rescue dogs and describes herself as a "huge animal-lover".^[83]

In April 2012, Gomez was named ambassador to the Ryan Seacrest Foudation^[84].

Entrepreneurship and sponsorships[link]

Gomez was part of Sears back-to-school fashion ad campaign.^[85] As part of the campaign Gomez was featured in the television commercials. In August 2009, Gomez also hosted the "Sears Arrive Air Band Casting Call" – to select five people for the first-ever "Sears Air Band", which performed at the 2009 MTV Video Music Awards.^[86]

In October 2008, Gomez launched her own production company, July Moon Productions, and partnered with XYZ Films to create star vehicles for Gomez. As part of the agreement Gomez will have the opportunity to be able option articles, hire writers and create talent packages to shop to studios.^[87][88] Also, as part of the deal, "XYZ Films will allow Gomez to star in and produce at least two films.^[81] Variety reported that: "In August, XYZ [Films] inked a similar deal with Time Inc. and management-production company the Collective to finance the development of the print media giant's content for the bigscreen [...] As part of the July Moon-XYZ deal, [Selena] Gomez will have the ability to cherry-pick projects from the vast Time Inc. library, which includes Time, Sports Illustrated, Fortune and Life."^[88]

In October 2009, Gomez announced her plan to launch her own fashion line, called "Dream Out Loud by Selena Gomez". The clothing line launched in the fall of 2010.^[89][90] The collection consists of and features bohemian dresses, floral tops, jeans, skirts, jackets, scarves and hats, all made from recycled or eco-friendly materials.^[91][92] Gomez said that the line will reflect her own personal style and described the clothing as being "pretty, feminine, and bohemian," and: "With my line, I really want to give the customer options on how they can put their own looks together [...] I want the pieces that can be easy to dress up or down, and the fabrics being eco-friendly and organic is super important [...] Also, the tags will all have some of my inspirational quotes on them. I'm just looking to send a good message."^[89][92] Gomez, who has no background in fashion, teamed up with designers Tony Melillo and Sandra Campos, both who have worked with big-name fashion houses.^[90] Gomez said of the partnering: "When I met Tony and Sandra, I was instantly comfortable with them and now they are just like family to me ... They are so creative and I love how I can just call them up whenever and talk to them about everything, even if it's just about changing a button ... They've been so cool about everything."^{[89][90][91][92]} The brand will be manufactured by, Melillo and Campos teamed with New York-based Adjmi Apparel and formed by Adjmi CH Brands LLC; which is the holding company for the brand.^[93]

It was announced on July 14, 2011, that Gomez had signed a license agreement with Adrenalina, an extreme sports and adventure-themed lifestyle brand, to develop, manufacture, and distribute the actress' fragrance. It is expected to debut in May of 2012. Chairman and C.E.O. of Adrenalina, Ilia Lekach, said, "We are incredibly enthused to be working with Ms. Gomez and will reveal more details pertaining to the fragrance as we get closer to the launch date."^[94]

Personal life and Image[link]

With a solid fan and media following, Selena Gomez is considered a teen idol. She has appeared on several magazine covers, including People Magazine,^[95] Cosmopolitan,^[96] Billboard,^[97] TVGuide,^[98] Teen Vogue,^[99] Seventeen,^[100] Elle^[101].

Wax statues of Gomez are on display at Madame Tussauds wax museums in New York^[102], London^[103], Washington D.C^[104] and Hollywood.

Relationships[link]

Gomez has had several high-profile relationships. She had an on-off relationship with singer Nick Jonas of the Jonas Brothers from 2008 to 2010.^[105] In 2009, she met actor Taylor Lautner in Vancouver, while she was filming Ramona and Beezus and he was shooting New Moon^[106], and the two dated for almost a year. However the pressure of the media became too much for them and caused the two to break-up.^[107] On February 27 2011, Gomez attended the 2011 Vanity Fair Oscar Party with Canadian singer Justin Bieber,^[108] confirming several months of media speculation about a romantic relationship between the pair.^{[109][110][111][112][113][114]} The relationship has since continued to garner significant media attention.^{[115][116][117][118][119]}

Filmography[link]

Film[link]

Television[link]

Discography[link]

Albums

• 2009: Kiss & Tell
• 2010: A Year Without Rain
• 2011: When the Sun Goes Down

Soundtrack albums[link]

Singles[link]

Featured singles[link]

Other charted songs[link]

Music videos[link]

Tours[link]

Rankings[link]

Awards and nominations[link]

Main article: List of awards and nominations received by Selena Gomez

References[link]

External links[link]

Wikimedia Commons has media related to: Selena Gomez

• Official website
• Selena Gomez at the Internet Movie Database
• Selena Gomez on Facebook
• Selena Gomez at Disney.com

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]