Element (mathematics)

In mathematics, an element, or member, of a set is any one of the distinct objects that make up that set.

Sets

Writing A = {1, 2, 3, 4} means that the elements of the set A are the numbers 1, 2, 3 and 4. Sets of elements of A, for example {1, 2}, are subsets of A.

Sets can themselves be elements. For example, consider the set B = {1, 2, {3, 4}}. The elements of B are not 1, 2, 3, and 4. Rather, there are only three elements of B, namely the numbers 1 and 2, and the set {3, 4}.

The elements of a set can be anything. For example, C = { red, green, blue }, is the set whose elements are the colors red, green and blue.

Notation and terminology

The relation "is an element of", also called set membership, is denoted by the symbol "∈". Writing

means that "x is an element of A". Equivalent expressions are "x is a member of A", "x belongs to A", "x is in A" and "x lies in A". The expressions "A includes x" and "A contains x" are also used to mean set membership, however some authors use them to mean instead "x is a subset of A". Logician George Boolos strongly urged that "contains" be used for membership only and "includes" for the subset relation only.

Taylor Swift

Taylor Alison Swift (born December 13, 1989) is an American singer-songwriter. Raised in Wyomissing, Pennsylvania, she moved to Nashville, Tennessee, at the age of 14 to pursue a career in country music. She signed with the independent label Big Machine Records and became the youngest songwriter ever signed by the Sony/ATV Music publishing house. The release of Swift's eponymous debut album in 2006 marked the start of her career as a country music singer. Her third single, "Our Song", made her the youngest person to single-handedly write and perform a number-one song on the Hot Country Songs chart.

Swift's second album, Fearless, was released in 2008. Buoyed by the pop crossover success of the singles "Love Story" and "You Belong with Me", Fearless became the best-selling album of 2009 in the United States. The album won four Grammy Awards, making Swift the youngest ever Album of the Year winner. Swift's third and fourth albums, 2010's Speak Now and 2012's Red, both sold more than one million copies within the first week of their U.S release. Speak Now's "Mean" won two Grammy Awards, while Red's singles "We Are Never Ever Getting Back Together" and "I Knew You Were Trouble" were successful worldwide. Swift's fifth album, the pop-focused 1989, was released in 2014 and sold more copies in its opening week than any album in the previous 12 years, making Swift the first and only act to have three albums sell more than one million copies in the opening release week. Its singles "Shake It Off", "Blank Space", and "Bad Blood" reached number one on the Billboard Hot 100. The album would go on to win three awards at the 2016 Grammys including Album of the Year making Swift the first and thus far only female artist to receive the award twice.

Flo Rida

Tramar Lacel Dillard (born September 16, 1979), better known by his stage name Flo Rida (pronounced /floʊ ˈraɪdə/,) is an American hip hop recording artist from Carol City, Florida. He is known for releasing a string of hits, such as his 2008 breakout single "Low", which was number one for 10 weeks in the United States and broke the record for digital download sales at the time of its release. "Low" was followed by the Top 40 hits, "Elevator" and "In the Ayer".

As of 2016, Flo Rida has released four studio albums. His first album, 2008's Mail on Sunday, debuted at number four in the US. The album was succeeded by R.O.O.T.S., the next year. His subsequent albums, 2010's Only One Flo (Part 1) and 2012's Wild Ones, also charted on the US Billboard 200 chart.

Flo Rida has sold over 80 million records worldwide. His catalog includes the international hit singles "Right Round", "Club Can't Handle Me", "Good Feeling", "Wild Ones", "Whistle", "I Cry" and "G.D.F.R.", among others.

Life and career