In mathematics and logic, the phrase "there is one and only one" is used to indicate that exactly one object with a certain property exists. In mathematical logic, this sort of quantification is known as uniqueness quantification or unique existential quantification.

Uniqueness quantification is often denoted with the symbols "∃!" or ∃₌₁". For example, the formal statement

may be read aloud as "there is exactly one natural number n such that n - 2 = 4".

Proving uniqueness turns out to be mostly easier than that of existence or expressibility. The most common technique to proving uniqueness is to assume there exists two quantities (say, a and b) that satisfies the condition given, and then logically deducing their equality, i.e. a = b.

As a simple high school example, to show x + 2 = 5 has only one solution, we assume there are two solutions first, namely, a and b, satisfying x + 2 = 5. Thus

By transitivity of equality,

By cancellation,

This simple example shows how a proof of uniqueness is done, the end result being the equality of the two quantities that satisfy the condition. We must say, however, that existence/expressibility must be proven before uniqueness, or else we cannot even assume the existence of those two quantities to begin with.

Long hair is a hairstyle. Exactly what constitutes long hair can change from culture to culture, or even within cultures. For example, a woman with chin-length hair in some cultures may be said to have short hair, while a man with the same length of hair in some of the same cultures would be said to have long hair.

Scientists view long hair as playing a large part in natural selection among many species, since long, thick and healthy hair or fur is frequently a sign of fertility and youth. As hair grows slowly, long hair reveals several years of a person's health status and reproductive fitness. Hair length is significantly correlated with female attractiveness, as rated by men as well as women. Hair length and quality can act as a cue to especially a woman's youth and health, signifying reproductive potential. The prevalence of trichophilia (hair partialism or fetischism) is 7% in the population, and very long hair is a common subject of devotion in this group.

Ways of life often viewed as more rigid, such as soldiers and religious cultures, often have explicit rules regarding hair length. For example, Buddhist monks shave their heads as part of their order of worship. Even outside religious structures, cultures often associate male long hair with ways of life outside of what is culturally accepted. Subservient cultures, for example, are sometimes detected by their rulers through hair length, as was the case with the Gaelic Irish under English rule and the Moors under Spanish rule in Medieval Spain.

Kate Moss (born 16 January 1974) is an English model who is known for her waifish figure and popularising the heroin chic look in the 1990s. She is also known for her controversial private life, high profile relationships, party lifestyle, and drug use. Moss changed the look of modelling and started a global debate on eating disorders, and her role in size zero fashion. In 2007, she came 2nd on the Forbes top-earning models list, estimated to have earned $9 million in one year.

Moss was born in Addiscombe, Croydon, London to Linda Rosina (Shepherd), a barmaid, and Peter Edward Moss, a travel agent. Kate has a younger brother named Nick and a half-sister named Lottie (Charlotte) and half-brother. Moss' parents divorced when she was 13. She attended Ridgeway Primary School and Riddlesdown Collegiate, but most commonly known as Riddlesdown High School, in Purley. She was not noted for her academic success but she did excel at sport.

Moss was discovered in 1988 at the age of 14 by Sarah Doukas, the founder of Storm Model Management, at JFK Airport in New York City, after a holiday in the Bahamas. Moss's career began when Corinne Day shot black-and-white photographs of her, styled by Melanie Ward, for British magazine The Face when she was 16, in a photo shoot titled "The 3rd Summer of Love". Day discovered Kate Moss when she was a young and unknown model and described the pictures that she took of Moss as ‘dirty realism’ or ‘grunge’.Moss then went on to become the "anti-supermodel" of the 1990s^{[citation needed]} in contrast to the "supermodels" of the moment^{[citation needed]}, such as Cindy Crawford, Elle Macpherson, Claudia Schiffer, and Naomi Campbell, who were known^{[citation needed]} for their curvaceous and tall figures.

DJ Fresh (born as Daniel Stein) is an English Drum & Bass and Dubstep producer and DJ. He was one of the principal members of drum & bass supergroup, Bad Company, alongside Darren White (dBridge), Jason Maldini, and Michael Wojcicki (Vegas). He also owns and runs the pioneering drum & bass label Breakbeat Kaos with Adam F.

Along with the three other members of Bad Company, Fresh founded the record label BC Recordings, as well as the website Dogs On Acid. Bad Company are heralded as one of the finest drum & bass acts ever, having produced numerous genre-defining tracks. Undoubtedly their most renowned track is "The Nine", a track released in 1998 when Fresh was just 21 years old. "The Nine" was later voted the greatest drum & bass track of all time by readers of Knowledge Magazine

Resuming his solo career in 2002, Fresh founded Breakbeat Punk, which merged with Adam F's Kaos Recordings to become Breakbeat Kaos in 2003. In 2004 Dogs on Acid was given its own imprint.

Fresh has worked with artists ranging from Pet Shop Boys, DJ Shadow, Apollo 440 to Andy C and Grooverider, and has also held a working relationship with the drum and bass trio Pendulum, whom he signed to Breakbeat Kaos in 2005.

Frederick Antony Ravi Kumar Zacharias (born 1946) is an Indian-born, Canadian-American evangelical Christian apologist. Zacharias is the author of numerous Christian books, including Gold Medallion Book Award winner Can Man Live Without God? and bestsellers Light in the Shadow of Jihad and The Grand Weaver. He is the founder and chairman of the board of Ravi Zacharias International Ministries, host of the radio programs Let My People Think and Just Thinking, and visiting professor at Wycliffe Hall of Oxford, where he teaches apologetics and evangelism. Zacharias studied as a visiting scholar at Cambridge University and held the chair in Evangelism and Contemporary Thought at Alliance Theological Seminary from 1981 to 1984. Commentator Chuck Colson referred to Zacharias as "the great apologist of our time."

Zacharias was born in Madras, India. Zacharias claims descent from a woman (of the Nambudiri Brahmin caste) and a low caste Boatman. Missionaries spoke to one of his ancestors about Christianity and thereafter the family was converted. Zacharias grew up in a nominal Anglican household, and he himself was an atheist until the age of 17, when he unsuccessfully tried to commit suicide by swallowing poison. While in the hospital, a local Christian worker brought him a Bible and instructed his mother to read to him out of John 14. Zacharias says that it was John 14:19 that touched him and caused him to commit his life to Christ.