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The prime (′, Unicode U+2032, HTML Entity ′) is a symbol with many mathematical uses:
A double prime (″, Unicode U+2033, HTML Entity ″) is the equivalent of two prime characters, and is used for similar purposes:
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; some are capable, but only if a font that includes the symbol is installed or selected.) To avoid counting the number of primes, the notation ''f''(''n'')(''x'') can be used to denote the ''n''th derivative of ''f''(''x''), particularly when the numerical instance ''n'' is large. This is also mathematically useful as an abstraction of ''n'' as a variable. 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”. NON-MATHEMATICAL USES The prime can also be used in the Transliteration of some Language s, such as Russian , to denote Palatalization . In Physics , the prime is used to denote variables after an event. For example, ''v''A′ 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 Group s or Nucleic Acid s. 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 8859-1 is commonly assumed on IRC ), they are often respectively approximated by normal or Italic apostrophes and quotation marks. |
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