Division (mathematics)

In mathematics, especially in elementary arithmetic, division (denoted ÷ or / or —) is an arithmetic operation. Specifically, if b times c equals a, written:

where b is not zero, then a divided by b equals c, written:

For instance,

since

In the above expressions, a is called the dividend, b is called the divisor, and c is called the quotient; in the expression or a is also called the numerator and b is also called the denominator.

Conceptually, division of integers can be viewed in either of two distinct but related ways quotition and partition:

Indeterminate form

In calculus and other branches of mathematical analysis, limits involving an algebraic combination of functions in an independent variable may often be evaluated by replacing these functions by their limits; if the expression obtained after this substitution does not give enough information to determine the original limit, it is said to take on an indeterminate form. The term was originally introduced by Cauchy's student Moigno in the middle of the 19th century.

The indeterminate forms typically considered in the literature are denoted 0/0, ∞/∞, 0 × ∞, ∞ − ∞, 0⁰, 1^∞ and ∞⁰.

Discussion

The most common example of an indeterminate form occurs as the ratio of two functions, in which both of these functions tend to zero in the limit, and is referred to as "the indeterminate form 0/0". As x approaches 0, the ratios x/x³, x/x, and x²/x go to ∞, 1, and 0 respectively. In each case, if the limits of the numerator and denominator are substituted, the resulting expression is 0/0, which is undefined. So, in a manner of speaking, 0/0 can take on the values 0, 1 or ∞, and it is possible to construct similar examples for which the limit is any particular value.

Linkin Park

Linkin Park is an American rock band from Agoura Hills, California. Formed in 1996, the band rose to international fame with their debut album Hybrid Theory (2000), which was certified diamond by the RIAA in 2005 and multi-platinum in several other countries. Their following studio album Meteora continued the band's success, topping the Billboard 200 album chart in 2003, and was followed by extensive touring and charity work around the world. In 2003, MTV2 named Linkin Park the sixth-greatest band of the music video era and the third-best of the new millennium.Billboard ranked Linkin Park No. 19 on the Best Artists of the Decade chart. In 2012, the band was voted as the greatest artist of the 2000s in a Bracket Madness poll on VH1. In 2014, the band was declared as the Biggest Rock Band in the World Right Now by Kerrang!.

Having adapted nu metal and rap metal to a radio-friendly yet densely layered style in Hybrid Theory and Meteora, the band explored other genres in their next studio album, Minutes to Midnight (2007). The album topped the Billboard charts and had the third-best debut week of any album that year. The band continued to explore a wider variation of musical types in their fourth album, A Thousand Suns (2010), layering their music with more electronic sounds and beats. Their fifth album, Living Things (2012), combines musical elements from all of their previous records. Their sixth and most recent album, The Hunting Party (2014), returned to a heavier rock sound. The band has collaborated with several other artists, most notably with rapper Jay Z in their mashup EP Collision Course, and many others on the remix albums Reanimation and Recharged. Linkin Park has sold over 68 million albums worldwide and has won two Grammy Awards.