Prime (mark)
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apostrophe ( ' ) ( ’ ) |
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ampersand ( & ) |
- This article is not about the symbol for the set of prime numbers, ℙ.
The prime (′, Unicode U+2032, ′) is a symbol with many mathematical uses:
- A complement in set theory: A′ is the complement of the set A
- A point related to another (e.g., by a transformation T): A′ is related to A
- A first derivative or derived function: f′(x) is the first derivative of f(x)
- An arcminute or minute of time: 42′ means 42 arcminutes or minutes
- A foot: 7′ means 7 feet
A double prime (″, Unicode U+2033, ″) is the equivalent of two prime characters, and is used for similar purposes:
- A second derivative: f″(x) is the second derivative of f(x)
- An arcsecond or second of time: 42″ means 42 arcseconds or seconds
- An inch: 7″ means 7 inches
As an extension of the above symbols, the triple prime (‴, Unicode U+2034) and quadruple prime (⁗, Unicode U+2057) are often used to indicate the third and fourth derivative of a function, respectively. (Not all Web browsers can display these symbols.)
To avoid counting the number of primes, the notation f(n)(x) can be used to mean the nth derivative of f(x) when n is large.
History
The name "prime" is something of a misnomer. Through the early part of the 20th century, the notation "x′" was read "x prime" not because it was an "x" followed by a "prime symbol", but because it was the first in the series that continued with "x″" ("x second") and "x‴" ("x third"). It was only later, in the 1950s and 1960s, that the term "prime" began to be applied to the apostrophe symbol itself.
Non-mathematical uses
The prime can also be used in the transliteration of some languages, such as Russian, to denote palatalization.
In physics, the prime is used to denote variables after an event. For example, vA' would indicate the velocity of object A after an event.
In molecular biology, the prime is used to denote the positions of carbon on a ring of deoxyribose or ribose. The prime distinguishes places on these two chemicals, rather than places on other parts of DNA or RNA, like phosphate groups or nucleic acids. Thus, when indicating the direction of movement of an enzyme along a string of DNA, biologists will says that it moves from the 5' end to the 3' end, because these carbons are hanging from the ends of the molecule. Prime can also be used to indicate which position a molecule has attached to, such as "5′-monophosphate".
Representations
The prime symbol should not be confused with the apostrophe (', Unicode U+0027) or acute accent (´, Unicode U+00B4); the double prime should not be confused with the quotation mark (", Unicode U+0022).
When the character set used does not include the prime or double prime character (e.g. ISO Latin-1 is commonly assumed on IRC), they are often respectively approximated by normal or italic apostrophes and quotation marks.