In mathematics, there are several equivalent ways of defining the real numbers. One of them is that they form a complete ordered field that does not contain any smaller complete ordered field. Such a definition does not prove that such a complete ordered field exists, and the existence proof consists of constructing a mathematical structure that satisfies the definition.
Lamont Herbert Dozier was an American singer, songwriter, and record producer from Detroit, Michigan. He co-wrote and produced 14 US Billboard number-one hits and four number ones in the UK.
New jack swing, new jack, or swingbeat is a fusion genre of the rhythms and production techniques of hip hop and dance-pop, and the urban contemporary sound of R&B. Spearheaded by producers Teddy Riley and Bernard Belle, new jack swing was most popular from the late-1980s to early-1990s. Its influence, along with hip hop, seeped into pop culture.
Sheena Shirley Easton is a Scottish singer and actress. Easton came into the public eye in an episode of the first British musical reality television programme The Big Time: Pop Singer, which recorded her attempts to gain a record contract and her eventual signing with EMI Records.
Bad is the seventh studio album by the American singer and songwriter Michael Jackson. It was released on August 31, 1987, by Epic Records, nearly five years after Jackson's previous album, Thriller (1982). Written and recorded between January 1985 and July 1987, Bad was the third and final collaboration between Jackson and producer Quincy Jones, with Jackson co-producing and composing all but two tracks. Jackson notably adopted an edgy look and sound with Bad, departing from his signature groove-based style and high-pitched vocals. The album incorporates pop, rock, funk, R&B, dance, soul, and hard rock styles. Jackson also experimented with newer recording technology, including digital synthesizers and drum machines, resulting in a sleeker and more aggressive sound. Jackson wrote nine of the eleven songs on the album. Lyrical themes on the album include media bias, paranoia, racial profiling, romance, self-improvement, and world peace. The album features appearances from Siedah Garrett and Stevie Wonder.
James Edward Ingram was an American singer, songwriter and record producer. He was a two-time Grammy Award-winner and a two-time Academy Award nominee for Best Original Song. After beginning his career in 1973, Ingram charted eight Top 40 hits on the U.S. Billboard Hot 100 chart from the early 1980s until the early 1990s, as well as thirteen top 40 hits on the Hot R&B/Hip-Hop Songs chart. In addition, he charted 20 hits on the Adult Contemporary chart. He had two number-one singles on the Hot 100: the first, a duet with fellow R&B artist Patti Austin, 1982's "Baby, Come to Me" topped the U.S. pop chart in 1983; "I Don't Have the Heart", which became his second number-one in 1990 was his only number-one as a solo artist.
LeVert was an American R&B vocal group from Cleveland, Ohio, United States. Formed in 1983, LeVert was composed of Sean and Gerald Levert and Marc Gordon.
"You Keep Me Hangin' On" is a song written and composed by Holland–Dozier–Holland. It was first recorded in 1966 by American Motown girl group the Supremes, reaching number one on the Billboard Hot 100. American rock band Vanilla Fudge released a cover version in June of the following year, which reached number six on the Billboard Hot 100. English singer Kim Wilde covered "You Keep Me Hangin' On" in 1986, reaching number one on the Billboard Hot 100 in June 1987. In the first 32 years of the Billboard Hot 100 rock era, "You Keep Me Hangin' On" became one of six songs to reach number one by two different musical acts. In 1996, American country singer Reba McEntire's version reached number two on the US Billboard Hot Dance Club Play chart. The BBC ranked the Supremes' original song at number 78 on The Top 100 Digital Motown Chart, which ranks Motown releases by their all-time UK downloads and streams.
Faith is the debut solo studio album by the English singer George Michael, released on 30 October 1987 by Columbia Records and Epic Records. In addition to playing various instruments on the album, Michael wrote and produced every track on the recording except for one, "Look at Your Hands", which he co-wrote with David Austin. A "black" inspired pop-R&B album, Faith's songs include introspective lyrics, which generated controversies about Michael's personal relationships at that time.
Lisa Lisa and Cult Jam were an urban contemporary band and one of the first freestyle music groups to emerge from New York City in the 1980s. Cult Jam consisted of vocalist Lisa Lisa, guitarist/bassist Alex "Spanador" Moseley, and drummer/keyboardist Mike Hughes. They were assembled and initially produced by Full Force.
Rhythmic contemporary, also known as Rhythmic Top 40, Rhythmic CHR or rhythmic crossover, is a primarily American music-radio format that includes a mix of EDM, upbeat rhythmic pop, hip hop and upbeat R&B hits. Rhythmic contemporary never uses hard rock or country in its airplay, but it may occasionally use a reggae, Latin, reggaeton, or a urban contemporary gospel hit. Essentially, the format is a cross between mainstream radio and urban contemporary radio formats.
"Sign o' the Times" is the lead single from American musician Prince's 1987 album of the same name. Despite being negative in nature, the song was originally intended for two separate Prince albums meant to be released in 1986, that were both shelved: Dream Factory and Crystal Ball. Prince performed all vocals & instruments on the song. "Sign o' the Times" was reportedly written and composed on a Sunday, when Prince usually wrote his most introspective songs.
Alicia Michelle "Miki" Howard is an American singer and actress who had a string of top 10 hit songs in the mid-1980s and early 1990s, including "Baby, Be Mine" (1987), "Come Share My Love" (1986) and "Love Under New Management" (1990). "Ain't Nobody Like You" (1992) and "Ain't Nuthin' in the World" (1989) both peaked at number one on the U.S. Billboard Top R&B Singles chart.
"Lean on Me" is a song written and recorded by American singer-songwriter Bill Withers. It was released in April 1972 as the first single from his second album, Still Bill. It was a number one single on both the soul singles and the Billboard Hot 100; the latter chart for three weeks in July 1972. Billboard ranked it as the No. 7 song of 1972. It was ranked number 208 on Rolling Stone's list of "The 500 Greatest Songs of All Time" in 2010. Numerous other versions have been recorded, and it is one of only nine songs to have reached No. 1 on the Billboard Hot 100 with versions recorded by two different artists.
Characters is the twenty-first studio album by American singer-songwriter Stevie Wonder, released in late 1987. The album features six singles including the Grammy-nominated "Skeletons" (#19) and "You Will Know" (#77), which both reached number one on the Billboard R&B Singles chart. The album also contained a duet with Michael Jackson, "Get It" (#80), that was a minor hit.
"Looking for a New Love" is a song by American dance-pop singer Jody Watley. It was released in January 1987 as the first single from her eponymous debut album. The song became one of the biggest pop and R&B singles of 1987. Watley re-recorded and re-issued the song in various remixes in 2005.
"Skeletons" is a number-one R&B single performed by American recording artist Stevie Wonder from his 1987 Characters album.
In mathematics, a matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object.