The prime symbol , double prime symbol , triple prime symbol , and quadruple prime symbol are used to designate units and for other purposes in
mathematics,
science
Science is a systematic endeavor that Scientific method, builds and organizes knowledge in the form of Testability, testable explanations and predictions about the universe.
Science may be as old as the human species, and some of the earli ...
,
linguistics
Linguistics is the scientific study of human language. It is called a scientific study because it entails a comprehensive, systematic, objective, and precise analysis of all aspects of language, particularly its nature and structure. Lingu ...
and
music
Music is generally defined as the The arts, art of arranging sound to create some combination of Musical form, form, harmony, melody, rhythm or otherwise Musical expression, expressive content. Exact definition of music, definitions of mu ...
.
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 ...
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
Typesetting is the composition of text by means of arranging physical ''type'' (or ''sort'') in mechanical systems or '' glyphs'' in digital systems representing '' characters'' (letters and other symbols).Dictionary.com Unabridged. Random ...
.
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
arcminute
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 a degree), and the double prime for
arcseconds ( 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 mathemati ...
s, 5
arcminutes and 30
arcseconds. 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 n ...
s, 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. 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 , 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
In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value). Derivatives are a fundamental tool of calculus. ...
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).
*
Set complement: is the complement of the set (other notation also exists).
* The negation of an
event in probability theory: (other notation also exists).
* The result of a
transformation:
* 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
In mathematics and physics, a vector space (also called a linear space) is a set whose elements, often called '' vectors'', may be added together and multiplied ("scaled") by numbers called '' scalars''. Scalars are often real numbers, but ...
The prime is said to "decorate" the letter to which it applies. The same convention is adopted in
functional programming
In computer science, functional programming is a programming paradigm where programs are constructed by applying and composing functions. It is a declarative programming paradigm in which function definitions are trees of expressions that ...
, particularly in
Haskell.
In
geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...
,
geography
Geography (from Greek: , ''geographia''. Combination of Greek words ‘Geo’ (The Earth) and ‘Graphien’ (to describe), literally "earth description") is a field of science devoted to the study of the lands, features, inhabitants, a ...
and
astronomy
Astronomy () is a natural science that studies astronomical object, celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and chronology of the Universe, evolution. Objects of interest ...
, prime and double prime are used as abbreviations for
minute and second of arc (and thus
latitude
In geography, latitude is a coordinate that specifies the north– south position of a point on the surface of the Earth or another celestial body. Latitude is given as an angle that ranges from –90° at the south pole to 90° at the north po ...
,
longitude
Longitude (, ) is a geographic coordinate that specifies the east– west position of a point on the surface of the Earth, or another celestial body. It is an angular measurement, usually expressed in degrees and denoted by the Greek let ...
,
elevation
The elevation of a geographic location is its height above or below a fixed reference point, most commonly a reference geoid, a mathematical model of the Earth's sea level as an equipotential gravitational surface (see Geodetic datum § ...
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 pai ...
).
In
physics
Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which rel ...
, 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, it is used to distinguish between different functional groups connected to an atom in a molecule, such as and , representing different
alkyl
In organic chemistry, an alkyl group is an alkane missing one hydrogen.
The term ''alkyl'' is intentionally unspecific to include many possible substitutions.
An acyclic alkyl has the general formula of . A cycloalkyl is derived from a cycloal ...
groups in an
organic compound
In chemistry, organic compounds are generally any chemical compounds that contain carbon- hydrogen or carbon-carbon bonds. Due to carbon's ability to catenate (form chains with other carbon atoms), millions of organic compounds are known. Th ...
. The
carbonyl
In organic chemistry, a carbonyl group is a functional group composed of a carbon atom double-bonded to an oxygen atom: C=O. It is common to several classes of organic compounds, as part of many larger functional groups. A compound containin ...
carbon in proteins is denoted as , which distinguishes it from the other
backbone carbon, the
alpha carbon, which is denoted as . In
physical chemistry
Physical chemistry is the study of macroscopic and microscopic phenomena in chemical systems in terms of the principles, practices, and concepts of physics such as motion, energy, force, time, thermodynamics, quantum chemistry, statistical ...
, it is used to distinguish between the lower state and the upper state of a
quantum number 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
Molecular biology is the branch of biology that seeks to understand the molecular basis of biological activity in and between cells, including biomolecular synthesis, modification, mechanisms, and interactions. The study of chemical and phys ...
, 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 ...
s. Thus, when indicating the direction of movement of an
enzyme
Enzymes () are proteins that act as biological catalysts by accelerating chemical reactions. The molecules upon which enzymes may act are called substrate (chemistry), substrates, and the enzyme converts the substrates into different molecule ...
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
Transliteration is a type of conversion of a text from one script to another that involves swapping letters (thus ''trans-'' + '' liter-'') in predictable ways, such as Greek → , Cyrillic → , Greek → the digraph , Armenian → or ...
of some
language
Language is a structured system of communication. The structure of a language is its grammar and the free components are its vocabulary. Languages are the primary means by which humans communicate, and may be conveyed through a variety of ...
s, such as
Slavic languages
The Slavic languages, also known as the Slavonic languages, are Indo-European languages spoken primarily by the Slavs, Slavic peoples and their descendants. They are thought to descend from a proto-language called Proto-Slavic language, Proto ...
, 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 historica ...
(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 "u ...
(the hard sign, ъ). However, in
ISO 9
ISO 9 is an international standard establishing a system for the transliteration into Latin characters of Cyrillic characters constituting the alphabets of many Slavic and non-Slavic languages.
Published on February 23, 1995 by the Internati ...
, the corresponding modifier letters are used instead.
Originally,
X-bar theory
In linguistics, X-bar theory is a model of phrase-structure grammar and a theory of syntactic category formation that was first proposed by Noam Chomsky in 1970Chomsky, Noam (1970). Remarks on Nominalization. In: R. Jacobs and P. Rosenbaum (eds.) ...
used a bar over syntactic units to indicate bar-levels in
syntactic structure, 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
Latex is an emulsion (stable dispersion) of polymer microparticles in water. Latexes are found in nature, but synthetic latexes are common as well.
In nature, latex is found as a milky fluid found in 10% of all flowering plants (angiosper ...
, 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
octaves from
middle C 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
A fermata (; "from ''fermare'', to stay, or stop"; also known as a hold, pause, colloquially a birdseye or cyclops eye, or as a grand pause when placed on a note or a rest) is a symbol of musical notation indicating that the note should be ...
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 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
Latex is an emulsion (stable dispersion) of polymer microparticles in water. Latexes are found in nature, but synthetic latexes are common as well.
In nature, latex is found as a milky fluid found in 10% of all flowering plants (angiosper ...
provides an oversized prime symbol, (
), which, when used in super- or sub-scripts, renders appropriately; e.g.,
f_\prime^\prime
appears as
. An apostrophe, , is a shortcut for a superscript prime; e.g., appears as
.
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 chartUnicode Spacing Modifier Letters code chart
{{Use dmy dates, date=May 2020
Mathematical symbols
Typographical symbols