A bijection is a function that is both injective (one-to-one) and surjective (onto). In other words, for every element in the domain of the function, there is a unique element in the codomain that it maps to, and every element in the codomain is mapped to by at least one element in the domain.
In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted i, called the imaginary unit and satisfying the equation ; every complex number can be expressed in the form , where a and b are real numbers. Because no real number satisfies the above equation, i was called an imaginary number by René Descartes. For the complex number , a is called the real part, and b is called the imaginary part. The set of complex numbers is denoted by either of the symbols or C. Despite the historical nomenclature "imaginary", complex numbers are regarded in the mathematical sciences as just as "real" as the real numbers and are fundamental in many aspects of the scientific description of the natural world.
In geometry and algebra, a real number is constructible if and only if, given a line segment of unit length, a line segment of length can be constructed with compass and straightedge in a finite number of steps. Equivalently, is constructible if and only if there is a closed-form expression for using only integers and the operations for addition, subtraction, multiplication, division, and square roots.
Robert Sylvester Kelly is an American convicted sex offender and former singer, songwriter, and record producer. He's been credited with prolific success in both R&B and hip hop, earning nicknames such as "the King of R&B", "the King of Pop-Soul", and the "Pied Piper of R&B". In 2022, he was convicted for sex trafficking, child pornography, and sexual exploitation of a minor.
Usher Raymond IV is an American singer, songwriter, and dancer. Primarily performing in the R&B genre, he debuted with his self-titled album Usher (1994), and rose to fame in the late 1990s with the release of his second album My Way (1997). It spawned his first Billboard Hot 100 number-one single "Nice & Slow", and saw similar success with its follow-ups "You Make Me Wanna..." and "My Way". His third album, 8701 (2001), saw continued success with the number one singles "U Remind Me" and "U Got It Bad", as well as the top-three single "U Don't Have to Call". It sold eight million copies worldwide and won his first two Grammy Awards as Best Male R&B Vocal Performance in 2002 and 2003.
Faith Renée Evans is an American R&B singer, songwriter and actress. Born in Lakeland, Florida, and raised in New Jersey, she relocated to Los Angeles in 1991 for a career in the music business. After working as a backing vocalist for Al B. Sure! and Christopher Williams, she became the first female artist to contract with Sean "Puff Daddy" Combs' Bad Boy Records in 1994 at age 20. On the label, she featured on records with several label mates such as 112 and Carl Thomas, and released three platinum-certified studio albums between 1995 and 2001: Faith (1995) and Keep the Faith (1998), and Faithfully (2001).
Tamia Marilyn Washington Hill is a Canadian singer and songwriter. Born and raised in Windsor, Ontario, Tamia performed in various singing and dancing competitions as a child. In 1994, after signing a development deal with Warner Bros. Records, she was asked by veteran producer Quincy Jones to appear on his album Q's Jook Joint (1995), earning her Grammy Award nominations for their collaboration on "You Put a Move on My Heart" and "Slow Jams". Her self-titled debut album was released in 1998 and followed by a series of successful albums with Elektra Records, including A Nu Day (2000) and More (2004). Several songs from these albums became hit singles on the pop and R&B record charts, including "So Into You", "Stranger in My House", and "Imagination", as well as her collaborations "Into You", "Missing You", and "Spend My Life with You".
K-Ci & JoJo is an American R&B duo, consisting of brothers Cedric "K-Ci" Hailey and Joel "JoJo" Hailey. Natives of Charlotte, North Carolina, they are also the lead singers of the chart-topping R&B group Jodeci with the DeGrate brothers—Donald and Mr. Dalvin. They are known for the 1997 smash hit "All My Life" which was the number-one song on the Billboard Hot 100 for three weeks. They also achieved mainstream success with the 1999 hit "Tell Me It's Real", which peaked at #2 on the Hot 100. Their 2001 song "Crazy" was included on the Save the Last Dance soundtrack and peaked at number eleven on the Billboard Hot 100.
My Way is the second studio album by American singer Usher. It was released on September 16, 1997, by LaFace Records in North America. The album features guest appearances from Monica, Jermaine Dupri, and Lil' Kim. The album was supported by three singles, all multi platinum-selling: "Nice & Slow", "My Way", and "You Make Me Wanna...".
Gerald Maxwell Rivera, known mononymously as Maxwell, is an American singer, songwriter, and record producer. He rose to prominence following the release of his debut studio album Maxwell's Urban Hang Suite (1996), which received widespread acclaim, and spawned the singles "Ascension " and "Sumthin' Sumthin'". The album has since been cited by music critics for helping form the "neo soul" movement that gained popularity during the late 1990s.
"You Make Me Wanna..." is a song by American recording artist Usher. It was released on August 5, 1997, by LaFace Records and Arista Records as the lead single from Usher's second studio album, My Way (1997). "You Make Me Wanna..." was written by Usher along with Jermaine Dupri and Manuel Seal, who both produced the tune. An R&B, soul and pop song in C minor, it makes use of acoustic guitar, hi-hat and bell instrumentation. The song focuses on a love triangle relationship, with the protagonist wishing to leave his girlfriend for his erstwhile best friend, with a hook in which Usher states, "You make me wanna leave the one I'm with and start a new relationship with you". The record won a Billboard Music Award, a Soul Train Music Award, and a WQHT Hip Hop Award, and was nominated for a Grammy Award.
"Doo Wop (That Thing)" is a song by American recording artist Lauryn Hill for her debut solo studio album The Miseducation of Lauryn Hill (1998). It was written and produced by Hill. The song was released as the lead single from The Miseducation of Lauryn Hill on August 10, 1998, by Ruffhouse Records and Columbia Records. No commercial release was originally intended for the single in the US, but limited-quantity physical formats were issued two months later, on October 27.
"The Thrill Is Gone" is a slow minor-key blues song written by West Coast blues musician Roy Hawkins and Rick Darnell in 1951. Hawkins's recording of the song reached number six in the Billboard R&B chart in 1951. In 1970, "The Thrill Is Gone" became a major hit for B.B. King. His rendition helped make the song a blues standard.
"Nobody's Supposed to Be Here" is a song by Canadian recording artist Deborah Cox, released as the lead single from her second studio album, One Wish (1998). Written by Montell Jordan and its producer, Anthony "Shep" Crawford, the song was released on the same day as the album, on September 15, 1998, by Arista Records. It is Cox's most successful song, peaking at number two on the Billboard Hot 100 for eight weeks and spending a then-record 14 weeks at number one on the Hot R&B/Hip-Hop Songs chart. In 2017, Billboard ranked the song at number five on its "Greatest of All Time Hot R&B/Hip-Hop Songs" chart.
"All My Life" is a song recorded by American R&B duo K-Ci & JoJo. The track was produced and written by Joel "JoJo" Hailey and Rory Bennett for K-Ci & JoJo's debut studio album, Love Always (1997). The song was released to airplay in January 1998 and was released physically on March 17, 1998, as the third single from the album through MCA Records. "All My Life" is an R&B and soul song. Music critics have claimed this as the duo's most successful song of their career.
"Friend of Mine" is a song recorded by singer Kelly Price. It spent five weeks at number 1 on the U.S. R&B chart and was awarded a Soul Train Music Award for Best R&B/Soul or Rap New Artist.
This is a list of the number-one albums of the UK R&B Singles and Albums Charts.