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.

A.C. Milan

Associazione Calcio Milan (Italian pronunciation: [assotʃatˈtsjoːne ˈkaltʃo ˈmiːlan]), commonly referred to as A.C. Milan or simply Milan, is a professional Italian football club based in Milan, Lombardy, that plays in Serie A. Milan was founded in 1899 by English lace-maker Herbert Kilpin and businessman Alfred Edwards among others. The club has spent its entire history, with the exception of the 1980–81 and 1982–83 seasons, in the top flight of Italian football, known as Serie A since 1929–30.

With 18 officially recognised UEFA and FIFA titles, they are the second most successful club in the world in terms of number of international titles, together with Boca Juniors and Real Madrid, and behind Al Ahly with twenty titles. Milan has won a joint record of three Intercontinental Cups and one of its successor, the FIFA Club World Cup. Milan have also won the European Cup/Champions League on seven occasions, second only to Real Madrid. They have also won the UEFA Super Cup a joint record five times and the Cup Winners' Cup twice. Milan has won every major competition in which it has competed, with the exception of the Europa League (in this competition they have lost two semi-finals in 1972 and in 2002). Domestically, with 18 league titles Milan is the joint-second most successful club in Serie A behind Juventus (31 titles), along with local rivals Inter. They have also won the Coppa Italia five times, as well as six Supercoppa Italiana triumphs.

Ronnie

Ronnie may refer to:

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.

Coppa Italia

The Coppa Italia (Italian for Italy Cup, officially known as TIM Cup because of its sponsorship) is an Italian football annual cup competition. Its first edition was held in 1922, but the second champions were not crowned until 1936. Juventus leads the way with ten wins, followed by Roma with nine. Roma has contested more finals, 17, while Juventus follow with 15. The holder can wear a "tricolore" cockade (Italian: coccarda), like the roundels that appear on military aircraft, and qualifies for a UEFA Europa League spot for the next season.

Format

The competition is a knockout tournament with pairings for each round made in advance; the draw for the whole competition is made before a ball is kicked. Each tie is played as a single leg, with the exception of the two-legged semi-finals. If a match is drawn, extra time is played. In the event of a draw after 120 minutes, a penalty shoot-out is contested. As well as being presented with the trophy, the winning team also qualifies for the UEFA Europa League (formerly named the UEFA Cup). If the winners have already qualified for the UEFA Champions League via Serie A, or are not entitled to play in UEFA competitions for any reason, the place goes to the next highest placed finisher in the league table.