Surjective function

In mathematics, a function f from a set X to a set Y is surjective (or onto), or a surjection, if every element y in Y has a corresponding element x in X such that f(x) = y. The function f may map more than one element of X to the same element of Y.

The term surjective and the related terms injective and bijective were introduced by Nicolas Bourbaki, a group of mainly French 20th-century mathematicians who under this pseudonym wrote a series of books presenting an exposition of modern advanced mathematics, beginning in 1935. The French prefix sur means over or above and relates to the fact that the image of the domain of a surjective function completely covers the function's codomain.

Definition

A surjective function is a function whose image is equal to its codomain. Equivalently, a function f with domain X and codomain Y is surjective if for every y in Y there exists at least one x in X with . Surjections are sometimes denoted by a two-headed rightwards arrow (U+21A0 ↠ RIGHTWARDS TWO HEADED ARROW), as in f : X ↠ Y.

Sean Paul

Sean Paul Ryan Francis Henriques (born 9 January 1973), known simply as Sean Paul, is a Jamaican dancehall ragga hip hop recording artist, musician, producer and actor.

Life and career

1973–1996: Early life

Sean Paul was born in Kingston, Jamaica to parents Garth and Frances, both of whom were talented athletes. His mother is a well-known painter. His paternal grandfather had Sephardi Jewish ancestry, from a family that had emigrated from Portugal, and his paternal grandmother was Afro-Caribbean; his mother is of English and Chinese Jamaican descent. Sean Paul was raised as a Catholic, though aware that his grandfather came from an old respected Jamaican Jewish family. Many members of his family are swimmers. His grandfather was on the first Jamaican men's national water polo team. His father also played water polo for the team in the 1960s, and competed in long-distance swimming, while Sean Paul's mother was a backstroke swimmer. Sean Paul played for the national water polo team from the age of 13 to 21, when he gave up the sport in order to launch his musical career. He attended Wolmer's Boys' School and the College of Arts, Science, and Technology, now known as the University of Technology, where he was trained in commerce with an aim of pursuing an occupation in hotel management.

Ben Affleck

Benjamin Geza Affleck-Boldt (born August 15, 1972), better known as Ben Affleck, is an American actor and filmmaker. He has won two Academy Awards and three Golden Globe Awards.

Affleck began his career as a child actor, starring in the PBS educational series The Voyage of the Mimi (1984, 1988). He later appeared in Dazed and Confused (1993) and various Kevin Smith films including Chasing Amy (1997) and Dogma (1999). Affleck gained fame when he and childhood friend Matt Damon won the Golden Globe and the Academy Award for Best Original Screenplay for Good Will Hunting (1997). He then starred in high-profile films including Armageddon (1998), Shakespeare in Love (1998), Pearl Harbor (2001), Changing Lanes (2002) and The Sum of All Fears (2002). After a career downturn, during which he appeared in Daredevil and the much-derided Gigli (both 2003), Affleck received a Golden Globe nomination for his performance in Hollywoodland (2006). In 2014, he starred in the psychological thriller Gone Girl. Affleck will portray Batman in Batman v Superman: Dawn of Justice and Suicide Squad (both 2016).

Matt Damon

Matthew Paige "Matt" Damon (/ˈdeɪmən/; born October 8, 1970) is an American actor and filmmaker. Born and raised in Cambridge, Massachusetts, Damon began his acting career by appearing in high school theater productions and he made his professional acting debut in the film Mystic Pizza (1988). He came to prominence in 1997 when he and Ben Affleck wrote and starred in Good Will Hunting, which won them the Academy Award for Best Original Screenplay and the Golden Globe Award for Best Screenplay and earned him a nomination for the Academy Award for Best Actor. He received further praise for his roles as the eponymous character in Saving Private Ryan (1998), the antihero in The Talented Mr. Ripley (1999), a fallen angel in Dogma, and received critical acclaim for performances in dramas such as Syriana (2005) and The Good Shepherd, as well as his role as a villain in the neo-noir crime drama The Departed (2006).

Damon is also known for his starring roles as Jason Bourne in the Bourne film series (2002–present).For his supporting role as rugby player Francois Pienaar in Invictus (2009) and his leading role as an astronaut stranded on Mars in The Martian (2015), he has received Academy Award nominations for Best Supporting Actor and Best Actor, respectively. Damon's leading role in The Martian won him the Golden Globe Award for Best Actor – Motion Picture Musical or Comedy. He has also received BAFTA, Golden Globe, and SAG nominations for Behind the Candelabra (2013) and three Emmy nominations for producing Project Greenlight