![]() ![]() The prime is said to "decorate" the letter to which it applies. The transpose of a matrix (other notation also exists). ![]() ![]() The result of a transformation: Tx = x′.The negation of an event in probability theory: Pr( A′) = 1 − Pr( A) (other notation also exists).Set complement: A′ is the complement of the set A (other notation also exists).Other notation for derivatives also exists (see Notation for differentiation). Similarly, if y = f ( x), then y′ and y″ are the first and second derivatives of y with respect to x. A derivative or differentiated function: in Lagrange's notation, f ′( x) and f ″( x) are the first and second derivatives of f ( x) with respect to x.Usually, the meaning of x′ is defined when it is first used, but sometimes, its meaning is assumed to be understood: For example, if a point is represented by the Cartesian coordinates ( x, y), then that point rotated, translated or reflected might be represented as ( x′, y′). In mathematics, the prime is generally used to generate more variable names for similar things without resorting to subscripts, with x′ generally meaning something related to (or derived from) x. Use in mathematics, statistics, and science This notation only applies to duration, and is seldom used for durations longer than 60 minutes. Primes are sometimes used to indicate minutes, and double primes to indicate seconds of time, as in the John Cage composition 4′33″ (spoken as "four thirty-three"), a composition that lasts exactly 4 minutes 33 seconds. In historical astronomical works, the triple prime was used to denote " thirds" ( 1⁄ 60 of an arcsecond) and a quadruple prime ⁗ " fourths" ( 1⁄ 60 of a third of arc), but modern usage has replaced this with decimal fractions of an arcsecond. ![]() As an angular measurement, 3° 5′ 30″ means 3 degrees, 5 arcminutes and 30 arcseconds. The prime symbol ′ is used for arcminutes ( 1⁄ 60 of a degree), and the double prime ″ for arcseconds ( 1⁄ 60 of an arcminute). The triple prime ‴ as used in watchmaking represents a ligne ( 1⁄ 12 of a French inch or pouce, about 2.26 millimetres or 0.089 inches). The prime symbol ′ is commonly used to represent feet (ft), and the double prime ″ is used to represent inches (in). See also: Positional notation § Sexagesimal system ![]()
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