Fractional part

The fractional part of a non‐negative real number is the excess beyond that number's integer part: . Here is the largest integer not greater than x, the floor of x. For a positive number written in a conventional positional numeral system (such as binary or decimal), the fractional part equals the digits appearing after the radix point. Equivalently, it equals the original number with the digits before the radix point substituted with 0.

There are various conflicting ways to extend the fractional part function to negative numbers. It is either defined as (Graham, Knuth & Patashnik 1992), as the part of the number to the right of the radix point, (Daintith 2004), or as the odd function:

Here, is the smallest integer not less than x, the ceiling of x. For example, the number −1.3 has a fractional part of 0.7 according to the first definition, 0.3 according to the second definition and −0.3 according to the third definition.

Under the first definition all real numbers can be written in the form where is the number to the left of the radix point, and the remaining fractional part is a nonnegative real number less than one. If is a positive rational number, then the fractional part of can be expressed in the form , where and are integers and . For example, if x = 1.05, then the fractional part of x is 0.05 and can be expressed as 5 / 100 = 1 / 20.

Grand Theft Auto V

Grand Theft Auto V is an open world, action-adventure video game developed by Rockstar North and published by Rockstar Games. It was released on 17 September 2013 for the PlayStation 3 and Xbox 360, on 18 November 2014 for the PlayStation 4 and Xbox One, and on 14 April 2015 for Microsoft Windows. The game is the first main entry in the Grand Theft Auto series since 2008's Grand Theft Auto IV. Set within the fictional state of San Andreas, based on Southern California, the single-player story follows three criminals and their efforts to commit heists while under pressure from a government agency. The open world design lets players freely roam San Andreas's open countryside and fictional city of Los Santos, based on Los Angeles.

The game is played from either a first-person or third-person view and its world is navigated on foot or by vehicle. Players control the three lead protagonists throughout single-player and switch between them both during and outside of missions. The story is centred on the heist sequences, and many missions involve shooting and driving gameplay. A "wanted" system governs the aggression of law enforcement response to players who commit crimes. Grand Theft Auto Online, the online multiplayer mode, lets up to 30 players explore the open world and engage in cooperative or competitive game matches.

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Grand Theft Auto

Grand Theft Auto or grand theft auto may refer to:

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