In mathematics, the limit inferior and limit superior of a sequence can be thought of as limiting bounds on the sequence. They can be thought of in a similar fashion for a function. For a set, they are the infimum and supremum of the set's limit points, respectively. In general, when there are multiple objects around which a sequence, function, or set accumulates, the inferior and superior limits extract the smallest and largest of them; the type of object and the measure of size is context-dependent, but the notion of extreme limits is invariant. Limit inferior is also called infimum limit, limit infimum, liminf, inferior limit, lower limit, or inner limit; limit superior is also known as supremum limit, limit supremum, limsup, superior limit, upper limit, or outer limit.
Mellon Collie and the Infinite Sadness is the third studio album by American alternative rock band the Smashing Pumpkins, released on October 24, 1995, in the United Kingdom and a day later in the United States on Virgin Records. Produced by frontman Billy Corgan with Flood and Alan Moulder, the 28-track album was released as a two-disc CD and triple LP. The album features a wide array of styles, as well as greater musical input from bassist D'arcy Wretzky and second guitarist James Iha.
Mark Ellis, known by his professional pseudonym Flood, is a British post-punk and alternative rock record producer and audio engineer. Flood's list of work includes projects with New Order, U2, Nine Inch Nails, Marc and the Mambas, Depeche Mode, Gary Numan, Ministry, The Charlatans, Thirty Seconds to Mars, Erasure, Nick Cave and the Bad Seeds, PJ Harvey, Foals, a-ha, Orbital, Sigur Rós, The Smashing Pumpkins, The Killers, White Lies, Pop Will Eat Itself, Warpaint and EOB. His co-production collaborations have included projects with Brian Eno, Daniel Lanois, Steve Lillywhite, and longtime collaborator Alan Moulder, with whom he co-founded the Assault & Battery studio complex. In 2006, his work with U2 led to his sharing of the Grammy Award for Album of the Year for How to Dismantle an Atomic Bomb.
The Aeroplane Flies High is a five-disc box set released by American alternative rock band The Smashing Pumpkins in 1996. It contains expanded versions of the five singles from their album Mellon Collie and the Infinite Sadness and also included a 44-page booklet with pictures and writings by the band's lead singer Billy Corgan, as well as lyrics. A limited edition release, the box reached number 42 on the Billboard charts. Originally intended to be limited to 200,000 copies, Virgin Records produced more after the original run sold out due to overwhelming and unexpected demand. The album was remastered in 2013 under the supervision of frontman Billy Corgan and reissued on vinyl and as a CD/DVD box set.
Infinite is the debut studio album by American rapper Eminem. It was released on November 12, 1996, through Web Entertainment. Recording sessions took place at the Bass Brothers' studio, with production handled by Mr. Porter and Eminem himself. The album features guest vocals from fellow rappers Proof, Mr. Porter, Eye-Kyu, Three, and Thyme, as well as singer Angela Workman.
Empty Sky is the debut studio album by British singer-songwriter Elton John, released on 6 June 1969. It would not be released in the United States until January 1975, with different cover art, well after John's fame had been established internationally.
Godley & Creme were an English rock duo formed in Manchester in 1977 by Kevin Godley and Lol Creme. The pair began releasing music as a duo after their departure from the rock band 10cc. In 1979, they directed their first music video with the single "An Englishman in New York". After this, they became involved in the production of videos for artists such as Ultravox, the Police, Yes, Duran Duran, Frankie Goes to Hollywood and Wang Chung, as well as directing the ground-breaking video for their 1985 single "Cry". The duo split at the end of the 1980s. Both have since been involved in music videos, TV commercials, and sporadic music projects.
David M. Axelrod is an American political consultant and analyst and former White House official. He is best known for being the chief strategist for Barack Obama's presidential campaigns. After Obama's election, Axelrod was appointed as Senior Advisor to the President. He left the position in early 2011 and became the Senior Strategist for Obama's successful re-election campaign in 2012. Axelrod wrote for the Chicago Tribune, and joined CNN as Senior Political Commentator in 2015. As of December 2019, Axelrod serves as the director of the non-partisan University of Chicago Institute of Politics. His memoir is titled Believer: My Forty Years in Politics.
Empire Burlesque is the 23rd studio album by American singer-songwriter Bob Dylan, released on June 10, 1985 on Columbia Records. Self-produced, the album peaked at No. 33 in the U.S. and No. 11 in the UK.
David Axelrod was an American composer, arranger, and producer. After starting out as a staff producer for record companies specializing in jazz, Axelrod became known by the mid-1960s in soul and jazz circles for his recording skills. In 1968, Axelrod embarked on a solo career and released several albums during the 1970s that showcased his characteristic sound, which combined heavily microphoned drums and baroque orchestration, and avant garde themes ranging from the environment to heightened mental awareness.
Song of Innocence is the debut album by American composer and producer David Axelrod. It was released in October 1968 by Capitol Records.
Bloodshy & Avant are a Swedish songwriting and production duo consisting of Christian "Bloodshy" Karlsson and Pontus "Avant" Winnberg. They have worked with many prominent artists, including Britney Spears, Kylie Minogue, Ms. Dynamite, Madonna, Jennifer Lopez, Katy Perry, Kelis, Girls' Generation, Christina Milian, Sky Ferreira, Utada and BoA. In addition to their production work, Karlsson and Winnberg are also members of the synth-pop group Miike Snow, alongside lead vocalist Andrew Wyatt.
65daysofstatic are an experimental band from Sheffield, England. Formed in 2001, the band is composed of instrumentalists Paul Wolinski, Joe Shrewsbury, Rob Jones and Simon Wright.
Rabbit in the Moon is an American electronic music group that formed in 1991. Their style draws from psychedelic trance, house music and breakbeat, along with other diverse influences.
Christopher P. Thomas is an English record producer who has worked extensively with the Beatles, Pink Floyd, Procol Harum, Roxy Music, Badfinger, Elton John, Paul McCartney, Pete Townshend, Pulp and the Pretenders. He has also produced breakthrough albums for the Sex Pistols, the Climax Blues Band and INXS. He worked on the initial sessions for How to Dismantle an Atomic Bomb by U2.
Pop Life is the fifth studio album by English girl group Bananarama, released on 13 May 1991 by London Records. It is the only album released which features Jacquie O'Sullivan, who replaced Siobhan Fahey in Bananarama upon her departure in 1988. This album marks the end of the group's association with the Stock Aitken Waterman production team as most of Pop Life was produced by Youth. English singer Zoë provided backing vocals on "Long Train Running". This would be the last album by Bananarama as a trio.
Stephen John Anderson is a British musician, songwriter and record producer, whose most recognisable work is as Kylie Minogue's collaborator on her tours and previous albums. He has also worked on songs and albums for many recording artists such as Britney Spears, Westlife, Christophe Willem, Judy Tzuke and Susan Boyle.
Victor Axelrod is an American musician, producer, and audio engineer from Brooklyn, New York. Since the mid-1990s, he has worked primarily in the genres of reggae, Afrobeat and soul, recording and producing under his own name and using the alias Ticklah.
Songs of Experience is the second studio album by American composer and producer David Axelrod. It was released in October 1969 by Capitol Records. Axelrod composed, arranged, and produced the album while recording with session musicians such as guitarist Al Casey, drummer Earl Palmer, and conductor Don Randi.
Sex, Death & the Infinite Void is the second studio album by English rock band Creeper released on 31 July 2020 by Roadrunner Records. The album was produced by Wax Ltd's Xandy Barry and was inspired by their experiences touring the United States with Waterparks.
