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.

Manchester United F.C.

Manchester United Football Club is a professional football club based in Old Trafford, Greater Manchester, England, that competes in the Premier League, the top flight of English football. Founded as Newton Heath LYR Football Club in 1878, the club changed its name to Manchester United in 1902 and moved to Old Trafford in 1910.

Manchester United have won 20 league titles, the most of any English club, 11 FA Cups, four League Cups and a record 20 FA Community Shields. The club has also won three European Cups, one UEFA Cup Winners' Cup, one UEFA Super Cup, one Intercontinental Cup and one FIFA Club World Cup. In 1998–99, the club became the first in the history of English football to achieve the treble of the Premier League, the FA Cup and the UEFA Champions League.

The 1958 Munich air disaster claimed the lives of eight players. In 1968, under the management of Matt Busby, Manchester United became the first English football club to win the European Cup. Alex Ferguson won 38 trophies, including 13 Premier League titles, 5 FA Cups and 2 UEFA Champions Leagues, between 1986 and 2013, when he announced his retirement. Louis van Gaal is the club's current manager after Ferguson's successor David Moyes was sacked after only 10 months in charge.

Popular culture

Popular culture or pop culture is the entirety of ideas, perspectives, attitudes, images, and other phenomena that are within the mainstream of a given culture, especially Western culture of the early to mid 20th century and the emerging global mainstream of the late 20th and early 21st century. Heavily influenced by mass media, this collection of ideas permeates the everyday lives of the society. The most common pop culture categories are: entertainment (movies, music, TV), sports, news (as in people/places in news), politics, fashion/clothes, technology, and slang.

Popular culture is often viewed as being trivial and "dumbed down" in order to find consensual acceptance throughout the mainstream. As a result, it comes under heavy criticism from various non-mainstream sources (most notably religious groups and countercultural groups) which deem it superficial, consumerist, sensationalist, or corrupt.

History and definitions

The term "popular culture" was coined in the 19th century or earlier. Traditionally, popular culture was associated with poor education and the lower classes, as opposed to the "official culture" and higher education of the upper classes.

Ben 10

Ben 10 is an American animated TV series and media franchise created by Man of Action Studios and produced by Cartoon Network Studios. The franchise revolves around a boy named Ben Tennyson who acquires a watch-like alien device, called the Omnimatrix, or more commonly, the Omnitrix, which allows the wearer to transform into multiple different alien creatures. The Ben 10 franchise has received wide critical acclaim, and the TV series has won three Emmy Awards. Worldwide, it has grossed over $4.5 billion in retail sales. The franchise has four movies, all of which aired on Cartoon Network between August 2007 and March 2014.

Series

Ben 10: (Original Series)

While on summer vacation, Ben stays with his grandfather, Max, and cousin, Gwen. During his stay, Ben discovers the Omnitrix, an alien device which allows him to turn into various extraterrestrial life forms. Ben uses the device to avert disasters, save people from terror, fight off hostile villains including Vilgax, an alien warlord bent on using the Omnitrix to outfit an alien army.

Video game

A video game is an electronic game that involves human interaction with a user interface to generate visual feedback on a video device such as a TV screen or computer monitor. The word video in video game traditionally referred to a raster display device, but it now implies any type of display device that can produce two- or three-dimensional images. Video games are sometimes believed to be a form of art, but this designation is controversial.

The electronic systems used to play video games are known as platforms; examples of these are personal computers and video game consoles. These platforms range from large mainframe computers to small handheld computing devices. Specialized video games such as arcade games, while common in the 1980s, have gradually declined in use due to the widespread availability of home video game devices (e.g., PlayStation 4 and Xbox One) and video games on desktop and laptop computers and smartphones.

The input device used for games, the game controller, varies across platforms. Common controllers include gamepads, mouses, keyboards, joysticks, the touchscreens of mobile devices and buttons. In addition to video and (in most cases) audio feedback, some games include haptic, vibration or force feedback peripherals.