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.

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.

Copa Argentina

The Copa Argentina (English: Argentine Cup), officially known as the "Copa Argentina Sancor Seguros" due to sponsorship reasons, is an official tournament organized by Argentine Football Association (AFA), with the aim of qualifying one club to the Copa Libertadores. The first editions of the championship were contested by teams in Primera División that did not earn eligibility to participate in the Copa Libertadores of the following year, and by the best clubs in the regional leagues.

The tournament was re-launched in 2011, with teams of all divisions that form the Argentine football league system taking part of the championship.

Boca Juniors is the most successful team with three titles, (1969, 2012 and 2015).

History

A new international competition, Copa Ganadores de Copa, would be held by CONMEBOL in 1970 as the South American equivalence of UEFA Cup Winners' Cup. AFA thus started a cup competition, the Copa Argentina, in 1969 and the winner would qualify for the Copa Ganadores de Copa 1970.