Prime (symbol)
From Wikipedia, the free encyclopedia
- This article is about the prime symbol. For the prime numbers, see prime number.
| Punctuation |
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apostrophe ( ', ’ ) |
| Interword separation |
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spaces ( ) ( ) ( ) |
| General typography |
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ampersand ( & ) |
| Uncommon typography |
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asterism ( ⁂ ) |
The prime symbol (′, Unicode U+2032, HTML entity ′) is commonly used to represent inches and feet, arcminutes and arcseconds, and sometimes minutes and seconds of time. 3′ 5″ could mean 3 feet and 5 inches (three foot five), or 3 minutes and 5 seconds. In watchmaking the triple prime ′′′ represents a ligne.
Calling the symbol "prime" is most common in mathematics (though it's sometimes called "dash" in the UK and Japan). It is generally used to get more variable names for things which are similar, without resorting to subscripts — x′ generally means "something related to x". Usually, the meaning of x′ is defined when it is first used, but sometimes its meaning is assumed to be understood:
- A derivative or derived function: f′(x) and f″(x) are the first and second derivatives of f(x) (other notation exists)
- Set complement: A′ is the complement of the set A (other notation exists)
- Negation of an Event (probability theory): Pr(A′) = 1 − Pr(A) (other notation exists)
- The result of a transformation: Tx = x′
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. It is also commonly used in relativity: The event at (x, y, z, t) in frame S has coordinates (x′, y′, z′, t′) in frame S′.
In chemistry, it is used to distinguish between different functional groups connected to an atom in a molecule, such as R and R′, representing different alkyl groups in a ketone.
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”.
The prime can also be used in the transliteration of some languages, such as Russian, to denote palatalization.
[edit] 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-like symbol itself. Although it is now more common to pronounce “x″” and “x‴” as “x double prime” or “x triple prime”, these are still sometimes pronounced in the old manner as “x second” and “x third”.
[edit] Representations
HTML also has the double prime (″, Unicode U+2033, ″), and Unicode has the triple prime (‴, Unicode U+2034) and quadruple prime (⁗, Unicode U+2057), which are more rarely used. Unicode defines double, triple, and quadruple primes as equivalent to consecutive (single) primes.
The characters modifier letter prime (ʹ, Unicode U+02B9) and modifier letter double prime (ʺ, Unicode U+02BA) are often used for linguistic purposes.
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 8859-1 is commonly assumed on IRC), they are often respectively approximated by normal or italic apostrophes and quotation marks. In LaTeX math mode, f' (f with an apostrophe) is rendered as f'. Furthermore, LaTeX provides an oversized prime symbol, \prime (
) for use in subscripts. For example, f_\prime^\prime appears as 
.
