Mathematical fallacy

In mathematics, certain kinds of mistaken proof are often exhibited, and sometimes collected, as illustrations of a concept of mathematical fallacy. There is a distinction between a simple mistake and a mathematical fallacy in a proof: a mistake in a proof leads to an invalid proof just in the same way, but in the best-known examples of mathematical fallacies, there is some concealment in the presentation of the proof. For example, the reason validity fails may be a division by zero that is hidden by algebraic notation. There is a striking quality of the mathematical fallacy: as typically presented, it leads not only to an absurd result, but does so in a crafty or clever way. Therefore, these fallacies, for pedagogic reasons, usually take the form of spurious proofs of obvious contradictions. Although the proofs are flawed, the errors, usually by design, are comparatively subtle, or designed to show that certain steps are conditional, and should not be applied in the cases that are the exceptions to the rules.

Atlético Madrid

Club Atlético de Madrid, SAD (Spanish pronunciation: [ˈkluβ aðˈletiko ðe maˈðɾið]) commonly known as Atlético de Madrid, or simply as Atlético, is a Spanish professional football club based in Madrid, that plays in La Liga.

In terms of importance of titles and number of followers, Atlético Madrid is the third most successful club in Spanish football, behind Real Madrid and Barcelona. In terms of the number of titles, Atlético Madrid is the fourth most successful club in Spanish football, behind Real Madrid, Barcelona and Athletic Bilbao. Atlético have won La Liga on ten occasions, including a league and cup double in 1996; the Copa del Rey on ten occasions; two Supercopas de España and one Copa Eva Duarte; in Europe, they won the European Cup Winners' Cup in 1962, were runners-up in 1963 and 1986, were European Cup runners-up in 1974 and 2014, won the Europa League in 2010 and in 2012, won the UEFA Super Cup in 2010 and 2012, won the Intertoto Cup in 2007, as well as the 1974 Intercontinental Cup.

Gorillaz

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Gorillaz are an English virtual band created in 1998 by Damon Albarn and Jamie Hewlett. The band consists of four animated members: 2D (lead vocals, keyboard), Murdoc Niccals (bass guitar), Noodle (guitar, keyboard, and backing vocals) and Russel Hobbs (drums and percussion). These members are completely fictional and are not personas of any "real life" musicians involved in the project. Their fictional universe is explored through the band's website and music videos, as well as a number of other media, such as short cartoons. The music is a collaboration between various musicians, with Albarn being the only permanent musical contributor. Writers and critics have described their music as alternative rock,Britpop,trip hop,hip hop,electronica, indie, dub, reggae and pop.

The band's 2001 debut album Gorillaz sold over seven million copies and earned them an entry in the Guinness Book of World Records as the Most Successful Virtual Band. It was nominated for the Mercury Prize in 2001, but the nomination was later withdrawn at the band's request. Their second studio album, Demon Days, released in 2005, went five times platinum in the UK,double platinum in the US, earned five Grammy Award nominations for 2006 and won one of them in the Best Pop Collaboration with Vocals category. The band has won numerous other awards, including two MTV Video Music Awards, an NME Award, three MTV Europe Music Awards, and have been nominated for nine Brit Awards. The combined sales of the Gorillaz and Demon Days albums had exceeded 15 million by 2007. The band's third studio album, Plastic Beach, was released in March 2010. Their latest album, The Fall, was released in December 2010 as a free download for fan club members, then in April 2011 as a physical release. Gorillaz plan to release new material in 2016.

Music video

A music video or song video is a short film integrating a song and imagery, produced for promotional or artistic purposes. Modern music videos are primarily made and used as a marketing device intended to promote the sale of music recordings. There are also cases where songs are used in tie in marketing campaigns that allow them to become more than just a song. Tie ins and merchandising could be used in toys are marketing campaigns for food and other products. Although the origins of music videos date back to musical short films that first appeared in the 1920s, they came into prominence in the 1980s when MTV based their format around the medium. Prior to the 1980s, these works were described by various terms including "illustrated song", "filmed insert", "promotional (promo) film", "promotional clip", "promotional video", "song video", "song clip" or "film clip". Since the creation and increased popularity of YouTube, mainstream artists now promote new music videos by releasing trailers of short promos on the site for their upcoming song and music video. Consequentially, YouTube has been converted into a social media platform for celebrities and artists to market themselves to their fans and audiences.