Double prime (symbol)
   HOME

TheInfoList



OR:

The prime symbol , double prime symbol , triple prime symbol , and quadruple prime symbol are used to designate units and for other purposes in
mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
, science, linguistics and music. Although the characters differ little in appearance from those of the
apostrophe The apostrophe ( or ) is a punctuation mark, and sometimes a diacritical mark, in languages that use the Latin alphabet and some other alphabets. In English, the apostrophe is used for two basic purposes: * The marking of the omission of one o ...
and single and double
quotation mark Quotation marks (also known as quotes, quote marks, speech marks, inverted commas, or talking marks) are punctuation marks used in pairs in various writing systems to set off direct speech, a quotation, or a phrase. The pair consists of an ...
s, the uses of the prime symbol are quite different. While an apostrophe is now often used in place of the prime, and a double quote in place of the double prime (due to the lack of prime symbols on everyday writing keyboards), such substitutions are not considered appropriate in formal materials or in typesetting.


Designation of units

The prime symbol is commonly used to represent feet (ft), and the double prime is used to represent inches (in). The triple prime as used in watchmaking represents a ( of a ''French'' inch or '' pouce'', about ). Primes are also used for angles. The prime symbol is used for arcminutes ( of a degree), and the double prime for
arcsecond A minute of arc, arcminute (arcmin), arc minute, or minute arc, denoted by the symbol , is a unit of angular measurement equal to of one degree. Since one degree is of a turn (or complete rotation), one minute of arc is of a turn. The na ...
s ( of an arcminute). As an angular measurement, means 3
degree Degree may refer to: As a unit of measurement * Degree (angle), a unit of angle measurement ** Degree of geographical latitude ** Degree of geographical longitude * Degree symbol (°), a notation used in science, engineering, and mathematics ...
s, 5
arcminutes A minute of arc, arcminute (arcmin), arc minute, or minute arc, denoted by the symbol , is a unit of angular measurement equal to of one degree. Since one degree is of a turn (or complete rotation), one minute of arc is of a turn. The na ...
and 30
arcsecond A minute of arc, arcminute (arcmin), arc minute, or minute arc, denoted by the symbol , is a unit of angular measurement equal to of one degree. Since one degree is of a turn (or complete rotation), one minute of arc is of a turn. The na ...
s. In historical astronomical works, the triple prime was used to denote " thirds" ( of an arcsecond) and a quadruple prime " fourths" ( of a third of arc), but modern usage has replaced this with decimal fractions of an arcsecond. Primes are sometimes used to indicate
minute The minute is a unit of time usually equal to (the first sexagesimal fraction) of an hour, or 60 seconds. In the UTC time standard, a minute on rare occasions has 61 seconds, a consequence of leap seconds (there is a provision to insert a nega ...
s, and double primes to indicate
second The second (symbol: s) is the unit of time in the International System of Units (SI), historically defined as of a day – this factor derived from the division of the day first into 24 hours, then to 60 minutes and finally to 60 seconds ...
s of time, as in the
John Cage John Milton Cage Jr. (September 5, 1912 – August 12, 1992) was an American composer and music theorist. A pioneer of indeterminacy in music, electroacoustic music, and non-standard use of musical instruments, Cage was one of the leading fi ...
composition ''
4′33″ ''4′33″'' (pronounced "four minutes, thirty-three seconds" or just "four thirty-three") is a three- movement composition by American experimental composer John Cage. It was composed in 1952, for any instrument or combination of instruments, ...
'' (spoken as "four thirty-three"), a composition that lasts exactly 4 minutes 33 seconds. This notation only applies to duration, and is seldom used for durations longer than 60 minutes.


Use in mathematics, statistics, and science

In mathematics, the prime is generally used to generate more variable names for similar things without resorting to subscripts, with generally meaning something related to (or derived from) . For example, if a point is represented by the
Cartesian coordinates A Cartesian coordinate system (, ) in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured in t ...
, then that point rotated, translated or reflected might be represented as . Usually, the meaning of is defined when it is first used, but sometimes, its meaning is assumed to be understood: * A derivative or differentiated function: in Lagrange's notation, and are the first and second derivatives of with respect to . Likewise are and . Similarly, if , then and are the first and second derivatives of with respect to . Other notation for derivatives also exists (see
Notation for differentiation In differential calculus, there is no single uniform notation for differentiation. Instead, various notations for the derivative of a function or variable have been proposed by various mathematicians. The usefulness of each notation varies with t ...
). *
Set Set, The Set, SET or SETS may refer to: Science, technology, and mathematics Mathematics *Set (mathematics), a collection of elements *Category of sets, the category whose objects and morphisms are sets and total functions, respectively Electro ...
complement: is the complement of the set (other notation also exists). * The negation of an
event Event may refer to: Gatherings of people * Ceremony, an event of ritual significance, performed on a special occasion * Convention (meeting), a gathering of individuals engaged in some common interest * Event management, the organization of eve ...
in probability theory: (other notation also exists). * The result of a
transformation Transformation may refer to: Science and mathematics In biology and medicine * Metamorphosis, the biological process of changing physical form after birth or hatching * Malignant transformation, the process of cells becoming cancerous * Trans ...
: * The transpose of a matrix (other notation also exists) *The
dual Dual or Duals may refer to: Paired/two things * Dual (mathematics), a notion of paired concepts that mirror one another ** Dual (category theory), a formalization of mathematical duality *** see more cases in :Duality theories * Dual (grammatical ...
of a vector space The prime is said to "decorate" the letter to which it applies. The same convention is adopted in functional programming, particularly in Haskell. In geometry, geography and astronomy, prime and double prime are used as abbreviations for
minute and second of arc A minute of arc, arcminute (arcmin), arc minute, or minute arc, denoted by the symbol , is a unit of angular measurement equal to of one degree. Since one degree is of a turn (or complete rotation), one minute of arc is of a turn. The na ...
(and thus latitude, longitude, elevation and
right ascension Right ascension (abbreviated RA; symbol ) is the angular distance of a particular point measured eastward along the celestial equator from the Sun at the March equinox to the (hour circle of the) point in question above the earth. When paired w ...
). In physics, the prime is used to denote variables after an event. For example, would indicate the velocity of object A after an event. It is also commonly used in relativity: the event at in frame , has coordinates in frame . In
chemistry Chemistry is the science, scientific study of the properties and behavior of matter. It is a natural science that covers the Chemical element, elements that make up matter to the chemical compound, compounds made of atoms, molecules and ions ...
, it is used to distinguish between different functional groups connected to an atom in a molecule, such as and , representing different alkyl groups in an organic compound. The carbonyl carbon in proteins is denoted as , which distinguishes it from the other backbone carbon, the alpha carbon, which is denoted as . In physical chemistry, it is used to distinguish between the lower state and the upper state of a
quantum number In quantum physics and chemistry, quantum numbers describe values of conserved quantities in the dynamics of a quantum system. Quantum numbers correspond to eigenvalues of operators that commute with the Hamiltonian—quantities that can be kno ...
during a transition. For example, denotes the upper state of the quantum number while denotes the lower state of the quantum number . 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 Ribonucleic acid (RNA) is a polymeric molecule essential in various biological roles in coding, decoding, regulation and expression of genes. RNA and deoxyribonucleic acid ( DNA) are nucleic acids. Along with lipids, proteins, and carbohydra ...
, like phosphate groups or
nucleic acid Nucleic acids are biopolymers, macromolecules, essential to all known forms of life. They are composed of nucleotides, which are the monomers made of three components: a 5-carbon sugar, a phosphate group and a nitrogenous base. The two main cl ...
s. Thus, when indicating the direction of movement of an enzyme along a string of DNA, biologists will say that it moves from the end to the end, because these carbons are on the ends of the DNA molecule. The chemistry of this reaction demands that the be extended by DNA synthesis. Prime can also be used to indicate which position a molecule has attached to, such as


Use in linguistics

The prime can be used in the transliteration of some languages, such as Slavic languages, to denote
palatalization Palatalization may refer to: *Palatalization (phonetics), the phonetic feature of palatal secondary articulation *Palatalization (sound change) Palatalization is a historical-linguistic sound change that results in a palatalized articulation ...
. Prime and double prime are used to transliterate Cyrillic
yeri Yeri may refer to: * Yeri, Cyprus * Yeri, Tajikistan *Yeri (singer) (born Kim Ye-rim, 1999), South Korean female singer, member of Red Velvet. *Yery Yeru or Eru (Ы ы; italics: ), usually called Y in modern Russian or Yery or Ery historic ...
(the soft sign, ь) and
yer A yer is either of two letters in Cyrillic alphabets, ъ (ѥръ, ''jerŭ'') and ь (ѥрь, ''jerĭ''). The Glagolitic alphabet used, as respective counterparts, the letters (Ⱏ) and (Ⱐ). They originally represented phonemically the "ult ...
(the hard sign, ъ). However, in ISO 9, the corresponding modifier letters are used instead. Originally, X-bar theory used a bar over syntactic units to indicate bar-levels in
syntactic structure In linguistics, syntax () is the study of how words and morphemes combine to form larger units such as phrases and sentences. Central concerns of syntax include word order, grammatical relations, hierarchical sentence structure ( constituency) ...
, generally rendered as an overbar. While easy to write, the bar notation proved difficult to typeset, leading to the adoption of the prime symbol to indicate a bar. (Despite the lack of bar, the unit would still be read as "X bar", as opposed to "X prime".) With contemporary development of typesetting software such as LaTeX, typesetting bars is considerably simpler; nevertheless, both prime and bar markups are accepted usages. Some X-bar notations use a double-prime (standing in for a double-bar) to indicate a phrasal level, indicated in most notations by "XP".


Use in music

The prime symbol is used in combination with lower case letters in the Helmholtz pitch notation system to distinguish notes in different
octave In music, an octave ( la, octavus: eighth) or perfect octave (sometimes called the diapason) is the interval between one musical pitch and another with double its frequency. The octave relationship is a natural phenomenon that has been refer ...
s from
middle C C or Do is the first note and semitone of the C major scale, the third note of the A minor scale (the relative minor of C major), and the fourth note (G, A, B, C) of the Guidonian hand, commonly pitched around 261.63  Hz. The actual frequen ...
upwards. Thus represents the below middle C, represents middle C, represents the in the octave above middle C, and the in the octave two octaves above middle C. A combination of upper case letters and sub-prime symbols is used to represent notes in lower octaves. Thus represents the below the bass stave, while represents the in the octave below that. In some musical scores, the double prime is used to indicate a length of time in seconds. It is used over a fermata denoting a long note or rest.


Computer encodings

Unicode and HTML representations of the prime and related symbols are as follows. * (lower case p) * (upper case P) * * * * * * * The "modifier letter prime" and "modifier letter double prime" characters are intended for linguistic purposes, such as the indication of stress or the transliteration of certain
Cyrillic , bg, кирилица , mk, кирилица , russian: кириллица , sr, ћирилица, uk, кирилиця , fam1 = Egyptian hieroglyphs , fam2 = Proto-Sinaitic , fam3 = Phoenician , fam4 = G ...
characters. In a context when the character set used does not include the prime or double prime character (e.g., in an online discussion context where only ASCII or
ISO 8859-1 ISO/IEC 8859-1:1998, ''Information technology — 8-bit single-byte coded graphic character sets — Part 1: Latin alphabet No. 1'', is part of the ISO/IEC 8859 series of ASCII-based standard character encodings, first edition published in 1 ...
SO Latin 1is expected), they are often respectively approximated by ASCII apostrophe (U+0027) or quotation mark (U+0022). LaTeX provides an oversized prime symbol, (\prime), which, when used in super- or sub-scripts, renders appropriately; e.g., f_\prime^\prime appears as f_\prime^\prime. An apostrophe, , is a shortcut for a superscript prime; e.g., appears as f'\,\!.


See also

* * * Rubik's Cube move notation, where the prime is used to invert moves or move sequences. * *


Notes


References


External links


Unicode General Punctuation code chart

Unicode Spacing Modifier Letters code chart
{{Use dmy dates, date=May 2020 Mathematical symbols Typographical symbols