Chess notation

Chess notation is the term for several systems that have developed to record either the moves made in a game of chess or the position of pieces on a chessboard. The earliest systems of notation used lengthy narratives to describe each move; these gradually evolved into terser notation systems. Currently algebraic chess notation is the accepted standard and is widely used. Algebraic notation has several variations. Descriptive chess notation was used in English- and Spanish-language literature until the late 20th century, but is now obsolete. There are some special systems for international correspondence chess. Portable Game Notation is used when working with computer chess programs. Systems also exist for transmission using Morse code over telegraph or radio.

Recording moves

Some move-recording notations are designed mainly for use by human players; others are designed for use by computers.

Notation systems for humans

In recognized competitions, all players are required to record all the moves of both players in order to resolve disputes about whether a player has made an illegal move and what the position should now be. In addition, if there is a time limit rule that requires each player to complete a specified number of moves in a specified time, as there is in most serious competition, an accurate count of the moves must be kept. All chess coaches strongly recommend the recording of one's games so that one can look for improvements in one's play. The algebraic and descriptive notations are also used in books about chess.

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.

Serie A

Serie A (Italian pronunciation: [ˈsɛːrje ˈa]), also called Serie A TIM due to sponsorship by Telecom Italia, is a professional league competition for football clubs located at the top of the Italian football league system and has been operating for over eighty years since the 1929–30 season. It had been organized by Lega Calcio until 2010, but a new league, the Lega Serie A, was created for the 2010–11 season. Serie A is regarded as one of the best football leagues in the world and it is often depicted as the most tactical national league. Serie A is the world's second strongest national league according to IFFHS and has produced the highest number of European Cup finalists: Italian clubs have reached the final of the competition on a record twenty-six different occasions, winning the title twelve times. Serie A is ranked 4th among European leagues according to UEFA's league coefficient behind La Liga, Bundesliga and Premier League, which is based on the performance of Italian clubs in the Champions League and the Europa League during the last five years. Serie A led the UEFA ranking from 1986 to 1988 and from 1990 to 1999.

Atlético Nacional

Club Atlético Nacional S. A., also known as Atlético Nacional, is a professional Colombian football team based in Medellín, that currently plays in the Categoría Primera A. Considered to be one of the strongest clubs from Colombia, it is one of the most consistent clubs in the country.

The club was founded on 7 March 1947 by former president of the league of Antioquia, Luis Alberto Villegas López. The club was first placed under the name of Club Atlético Municipal de Medellín. In 1996, the company in which administrated the club, Organización Ardila Lülle, officially acquired Nacional. Many Colombian legends have originated from Nacional such as René Higuita, Juan Camilo Zúñiga, Iván Córdoba, Juan Pablo Ángel, David Ospina and most noticeably, Andrés Escobar and Víctor Aristizábal, among many others.

They play their home games at the Atanasio Girardot stadium, with a capacity of over 40,000. They share the same stadium with local bitter rivals, Independiente Medellín, said rivalry is known as El Clásico Paisa. Infamous for its aggressive background, it is considered to be one of the most important derbies in Colombia, as well as one of the most important in South America. All while being recognized by FIFA as a 'classic' match-up. Nacional is also known to have rivalries with Millonarios by the El Clásico de la rivalidad regional derby, and América de Cali. Although these rivalries are based on rivaling success; with Millonarios originally being the club that had the most domestic trophies before Nacional surpassed their count in 2015, whereas America has met with Nacional on numerous occasions during league/cup finals.

Copa Libertadores

The Copa Libertadores de América (Portuguese: Copa Libertadores da América) is an annual international club football competition organized by CONMEBOL since 1960. It is one of the most prestigious tournaments in the world and the most prestigious club competition in Latin American football. The tournament is named in honor of the Libertadores (Spanish and Portuguese for liberators), the main leaders of the South American wars of independence, so a literal translation of its name into English would be "Liberators of America Cup".

It is sponsored by Bridgestone and is known as the Copa Bridgestone Libertadores. The competition has had several different formats over its lifetime. At the beginning, only the champions of the South American leagues participated. In 1966, the runners-up of the South American leagues began to join. In 1998, Mexican teams were invited to compete, and have contested regularly since 2000, when the tournament was expanded from 20 to 32 teams. Today at least three clubs per country compete in the tournament, while Argentina and Brazil each have five clubs participating. Traditionally, a group stage has always been used but the number of teams per group has varied several times.