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. Linguis ...

and

semiotics Semiotics (also called semiotic studies) is the systematic study of sign processes (semiosis) and meaning making. Semiosis is any activity, conduct, or process that involves signs, where a sign is defined as anything that communicates something, ...

, a notation is a

system A system is a group of interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its environment, is described by its boundaries, structure and purpose and express ...

of graphics or

symbol A symbol is a mark, sign, or word that indicates, signifies, or is understood as representing an idea, object, or relationship. Symbols allow people to go beyond what is known or seen by creating linkages between otherwise very different con ...

s, characters and abbreviated

expression Expression may refer to: Linguistics * Expression (linguistics), a word, phrase, or sentence * Fixed expression, a form of words with a specific meaning * Idiom, a type of fixed expression * Metaphorical expression, a particular word, phrase, ...

s, used (for example) in

artistic Art is a diverse range of human activity, and resulting product, that involves creative or imaginative talent expressive of technical proficiency, beauty, emotional power, or conceptual ideas. There is no generally agreed definition of what ...

and

scientific discipline The branches of science, also referred to as sciences, scientific fields or scientific disciplines, are commonly divided into three major groups: *Formal sciences: the study of formal systems, such as those under the branches of logic and mat ...

s to represent technical facts and quantities by convention. Therefore, a notation is a collection of related symbols that are each given an

arbitrary Arbitrariness is the quality of being "determined by chance, whim, or impulse, and not by necessity, reason, or principle". It is also used to refer to a choice made without any specific criterion or restraint. Arbitrary decisions are not necess ...

meaning, created to facilitate structured communication within a

domain knowledge Domain knowledge is knowledge of a specific, specialized discipline or field, in contrast to general (or domain-independent) knowledge. The term is often used in reference to a more general discipline—for example, in describing a software engin ...

field of study Field may refer to: Expanses of open ground * Field (agriculture), an area of land used for agricultural purposes * Airfield, an aerodrome that lacks the infrastructure of an airport * Battlefield * Lawn, an area of mowed grass * Meadow, a gras ...

. Standard notations refer to general agreements in the way things are written or denoted. The term is generally used in technical and scientific areas of study like mathematics,

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 relat ...

, chemistry and

biology Biology is the scientific study of life. It is a natural science with a broad scope but has several unifying themes that tie it together as a single, coherent field. For instance, all organisms are made up of cells that process hereditary ...

, but can also be seen in areas like

business Business is the practice of making one's living or making money by producing or buying and selling products (such as goods and services). It is also "any activity or enterprise entered into for profit." Having a business name does not separa ...

, economics and

music Music is generally defined as the art of arranging sound to create some combination of form, harmony, melody, rhythm or otherwise expressive content. Exact definitions of music vary considerably around the world, though it is an aspect ...

Written communication

Writing systems

* Phonographic

writing systems A writing system is a method of visually representing verbal communication, based on a script and a set of rules regulating its use. While both writing and speech are useful in conveying messages, writing differs in also being a reliable form ...

, by definition, use symbols to represent components of auditory language, i.e.

speech Speech is a human vocal communication using language. Each language uses phonetic combinations of vowel and consonant sounds that form the sound of its words (that is, all English words sound different from all French words, even if they are ...

, which in turn refers to things or ideas. The two main kinds of phonographic notational system are the

alphabet An alphabet is a standardized set of basic written graphemes (called letter (alphabet), letters) that represent the phonemes of certain spoken languages. Not all writing systems represent language in this way; in a syllabary, each character ...

and the

syllabary In the linguistic study of written languages, a syllabary is a set of written symbols that represent the syllables or (more frequently) moras which make up words. A symbol in a syllabary, called a syllabogram, typically represents an (optiona ...

. Some written languages are more consistent in their correlation of written symbols (or

grapheme In linguistics, a grapheme is the smallest functional unit of a writing system. The word ''grapheme'' is derived and the suffix ''-eme'' by analogy with ''phoneme'' and other names of emic units. The study of graphemes is called ''graphemics' ...

s) with sound (or

phoneme In phonology and linguistics, a phoneme () is a unit of sound that can distinguish one word from another in a particular language. For example, in most dialects of English, with the notable exception of the West Midlands and the north-west ...

s), and are therefore considered to have better

phonemic orthography A phonemic orthography is an orthography (system for writing a language) in which the graphemes (written symbols) correspond to the phonemes (significant spoken sounds) of the language. Natural languages rarely have perfectly phonemic orthographi ...

. * Ideographic writing, by definition, refers to things or ideas independently of their pronunciation in any language. Some ideographic systems are also

pictogram A pictogram, also called a pictogramme, pictograph, or simply picto, and in computer usage an icon, is a graphic symbol that conveys its meaning through its pictorial resemblance to a physical object. Pictographs are often used in writing and gr ...

s that convey meaning through their pictorial resemblance to a physical object.

Linguistics

* Various brackets, parentheses, slashes, and lines are used around words and letters in

to distinguish written from spoken forms, etc. See .

Biology and medicine

Nucleic acid notation The nucleic acid notation currently in use was first formalized by the International Union of Pure and Applied Chemistry (IUPAC) in 1970. This universally accepted notation uses the Roman characters G, C, A, and T, to represent the four nucleotide ...

* Systems Biology Graphical Notation (SBGN) * Sequence motif pattern-description notations * Cytogenetic notation *

Energy Systems Language The Energy Systems Language, also referred to as Energese, Energy Circuit Language, or Generic Systems Symbols, is a modelling language used for composing energy flow diagrams in the field of systems ecology. It was developed by Howard T. Odum ...

Chemistry

* A chemical formula describes a chemical compound using element symbols and subscripts, e.g. for water or for glucose * SMILES is a notation for describing the structure of a molecule with a

plain text In computing, plain text is a loose term for data (e.g. file contents) that represent only characters of readable material but not its graphical representation nor other objects ( floating-point numbers, images, etc.). It may also include a lim ...

string, e.g. N=N for nitrogen or CCO for ethanol

Computing

* BNF (Backus normal form, or

Backus–Naur form In computer science, Backus–Naur form () or Backus normal form (BNF) is a metasyntax notation for context-free grammars, often used to describe the syntax of languages used in computing, such as computer programming languages, document formats ...

) and EBNF (extended Backus-Naur form) are the two main notation techniques for context-free grammars. * Drakon-charts are a graphical notation of algorithms and procedural knowledge. *

Hungarian notation Hungarian notation is an identifier naming convention in computer programming, in which the name of a variable or function indicates its intention or kind, and in some dialects its type. The original Hungarian notation uses intention or kind in ...

is an identifier naming convention in computer programming, that represents the type or intended use of a variable with a specific pattern within its name. * Mathematical markup languages are computer notations for representing mathematical formulae. * Various notations have been developed to specify

regular expression A regular expression (shortened as regex or regexp; sometimes referred to as rational expression) is a sequence of characters that specifies a search pattern in text. Usually such patterns are used by string-searching algorithms for "find" or ...

s. * The APL programming language provided a rich set of very concise new notations

Logic

A variety of symbols are used to express logical ideas; see the

List of logic symbols In logic, a set of symbols is commonly used to express logical representation. The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics. Additionally, the sub ...

Management

* Time and motion study symbols such as therbligs

Mathematics

Mathematical notation Mathematical notation consists of using symbols for representing operations, unspecified numbers, relations and any other mathematical objects, and assembling them into expressions and formulas. Mathematical notation is widely used in mathema ...

is used to represent various kinds of mathematical ideas. ** All types of

notation in probability Probability theory and statistics have some commonly used conventions, in addition to standard mathematical notation and mathematical symbols. Probability theory * Random variables are usually written in upper case roman letters: ''X'', ''Y'', ...

Cartesian coordinate system 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 i ...

, for representing position and other spatial concepts in analytic geometry **

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 ...

, common representations of the

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. ...

calculus Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithm ...

Big O notation Big ''O'' notation is a mathematical notation that describes the limiting behavior of a function when the argument tends towards a particular value or infinity. Big O is a member of a family of notations invented by Paul Bachmann, Edmund Land ...

, used for example in analysis to represent less significant elements of an expression, to indicate that they will be neglected **

Z notation The Z notation is a formal specification language used for describing and modelling computing systems. It is targeted at the clear specification of computer programs and computer-based systems in general. History In 1974, Jean-Raymond Abrial ...

, a formal notation for specifying objects using

Zermelo–Fraenkel set theory In set theory, Zermelo–Fraenkel set theory, named after mathematicians Ernst Zermelo and Abraham Fraenkel, is an axiomatic system that was proposed in the early twentieth century in order to formulate a theory of sets free of paradoxes such a ...

and

first-order predicate logic First-order logic—also known as predicate logic, quantificational logic, and first-order predicate calculus—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantifie ...

Ordinal notation In mathematical logic and set theory, an ordinal notation is a partial function mapping the set of all finite sequences of symbols, themselves members of a finite alphabet, to a countable set of ordinals. A Gödel numbering is a function mapping t ...

Set-builder notation In set theory and its applications to logic, mathematics, and computer science, set-builder notation is a mathematical notation for describing a set by enumerating its elements, or stating the properties that its members must satisfy. Defini ...

, a formal notation for defining sets in

set theory Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly concer ...

* Systems to represent very large numbers **

Conway chained arrow notation Conway chained arrow notation, created by mathematician John Horton Conway, is a means of expressing certain extremely large numbers. It is simply a finite sequence of positive integers separated by rightward arrows, e.g. 2\to3\to4\to5\to6. As wit ...

Knuth's up-arrow notation In mathematics, Knuth's up-arrow notation is a method of notation for very large integers, introduced by Donald Knuth in 1976. In his 1947 paper, R. L. Goodstein introduced the specific sequence of operations that are now called ''hyperoperat ...

** Steinhaus–Moser notation **

Schläfli symbol In geometry, the Schläfli symbol is a notation of the form \ that defines regular polytopes and tessellations. The Schläfli symbol is named after the 19th-century Swiss mathematician Ludwig Schläfli, who generalized Euclidean geometry to more ...

in geometry *

Numeral system A numeral system (or system of numeration) is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner. The same sequence of symbo ...

s, notation for writing numbers, including **

Arabic numeral Arabic numerals are the ten numerical digits: , , , , , , , , and . They are the most commonly used symbols to write decimal numbers. They are also used for writing numbers in other systems such as octal, and for writing identifiers such as ...

s **

Roman numeral Roman numerals are a numeral system that originated in ancient Rome and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages. Numbers are written with combinations of letters from the Latin alphabet, ea ...

s **

Scientific notation Scientific notation is a way of expressing numbers that are too large or too small (usually would result in a long string of digits) to be conveniently written in decimal form. It may be referred to as scientific form or standard index form, o ...

for expressing large and small numbers **

Sign-value notation A sign-value notation represents numbers by a series of numeric signs that added together equal the number represented. In Roman numerals for example, X means ten and L means fifty. Hence LXXX means eighty (50 + 10 + 10 ...

, using signs or symbols to represent numbers **

Positional notation Positional notation (or place-value notation, or positional numeral system) usually denotes the extension to any base of the Hindu–Arabic numeral system (or decimal system). More generally, a positional system is a numeral system in which the ...

also known as place-value notation, in which each position is related to the next by a multiplier which is called the ''base'' of that numeral system ***

Binary notation A binary number is a number expressed in the base-2 numeral system or binary numeral system, a method of mathematical expression which uses only two symbols: typically "0" (zero) and "1" ( one). The base-2 numeral system is a positional notation ...

, a positional notation in base two ***

Octal The octal numeral system, or oct for short, is the base-8 number system, and uses the digits 0 to 7. This is to say that 10octal represents eight and 100octal represents sixty-four. However, English, like most languages, uses a base-10 number ...

notation, a positional notation in base eight, used in some computers ***

Decimal notation The decimal numeral system (also called the base-ten positional numeral system and denary or decanary) is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers of the Hindu–Arabic numer ...

, a positional notation in base ten ***

Hexadecimal In mathematics and computing, the hexadecimal (also base-16 or simply hex) numeral system is a positional numeral system that represents numbers using a radix (base) of 16. Unlike the decimal system representing numbers using 10 symbols, hexa ...

notation, a positional notation in base sixteen, commonly used in computers ***

Sexagesimal Sexagesimal, also known as base 60 or sexagenary, is a numeral system with sixty as its base. It originated with the ancient Sumerians in the 3rd millennium BC, was passed down to the ancient Babylonians, and is still used—in a modified form� ...

notation, an ancient numeral system in base sixty * See also

Table of mathematical symbols A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula. ...

- for general tokens and their definitions...

Physics

Bra–ket notation In quantum mechanics, bra–ket notation, or Dirac notation, is used ubiquitously to denote quantum states. The notation uses angle brackets, and , and a vertical bar , to construct "bras" and "kets". A ket is of the form , v \rangle. Mathemat ...

, or Dirac notation, is an alternative representation of probability distributions in

quantum mechanics Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, qu ...

. *

Tensor index notation In mathematics, Ricci calculus constitutes the rules of index notation and manipulation for tensors and tensor fields on a differentiable manifold, with or without a metric tensor or connection. It is also the modern name for what used to be ca ...

is used when formulating physics (particularly

continuum mechanics Continuum mechanics is a branch of mechanics that deals with the mechanical behavior of materials modeled as a continuous mass rather than as discrete particles. The French mathematician Augustin-Louis Cauchy was the first to formulate such m ...

, electromagnetism, relativistic quantum mechanics and field theory, and general relativity) in the language of

tensor In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects related to a vector space. Tensors may map between different objects such as vectors, scalars, and even other tenso ...

Typographical conventions

Infix notation Infix notation is the notation commonly used in arithmetical and logical formulae and statements. It is characterized by the placement of operators between operands—"infixed operators"—such as the plus sign in . Usage Binary relations are ...

, the common arithmetic and logical formula notation, such as "''a'' + ''b'' − ''c''". *

Polish notation Polish notation (PN), also known as normal Polish notation (NPN), Łukasiewicz notation, Warsaw notation, Polish prefix notation or simply prefix notation, is a mathematical notation in which operators ''precede'' their operands, in contrast t ...

or "prefix notation", which places the operator before the operands (arguments), such as "+ ''a'' ''b''". *

Reverse Polish notation Reverse Polish notation (RPN), also known as reverse Łukasiewicz notation, Polish postfix notation or simply postfix notation, is a mathematical notation in which operators ''follow'' their operands, in contrast to Polish notation (PN), in wh ...

or "postfix notation", which places the operator after the operands, such as "''a'' ''b'' +".

Sports and games

Baseball scorekeeping Baseball scorekeeping is the practice of recording the details of a baseball game as it unfolds. Professional baseball leagues hire official scorers to keep an official record of each game (from which a box score can be generated), but many fans k ...

, to represent a game of baseball * Aresti Catalogue, to represent aerobatic manoeuvres * Chess notation, to represent moves in a game of chess ** Algebraic notation ***

Portable Game Notation Portable Game Notation (PGN) is a standard plain text format for recording chess games (both the moves and related data), which can be read by humans and is also supported by most chess software. History PGN was devised around 1993, by Steven J. ...

Descriptive notation Descriptive notation is a chess notation system based on abbreviated natural language. Its distinctive features are that it refers to files by the piece that occupies the back rank square in the starting position and that it describes each square t ...

Forsyth–Edwards Notation Forsyth–Edwards Notation (FEN) is a standard notation for describing a particular board position of a chess game. The purpose of FEN is to provide all the necessary information to restart a game from a particular position. FEN is based on a sy ...

Siteswap Siteswap, also called quantum juggling or the Cambridge notation, is a numeric juggling notation used to describe or represent juggling patterns. The term may also be used to describe siteswap patterns, possible patterns transcribed using si ...

notation represents a juggling pattern as a sequence of numbers

Graphical notations

Music

Musical notation Music notation or musical notation is any system used to visually represent aurally perceived music played with instruments or sung by the human voice through the use of written, printed, or otherwise-produced symbols, including notation for ...

permits a composer to express musical ideas in a musical composition, which can be read and interpreted during performance by a trained musician; there are many different ways to do this (hundreds have been proposed), although

staff notation In Western musical notation, the staff (US and UK)"staff" in the Collins ...

provides by far the most widely used system of

modern musical symbols Musical symbols are marks and symbols in musical notation that indicate various aspects of how a piece of music is to be performed. There are symbols to communicate information about many musical elements, including pitch, duration, dynamics, o ...

Dance and movement

Benesh Movement Notation Benesh Movement Notation (BMN), also known as Benesh notation or choreology, is a dance notation system used to document dance and other types of human movement. Invented by Joan and Rudolf Benesh in the late 1940s, the system uses abstract sym ...

permits a graphical representation of human bodily movements * Laban Movement Analysis or

Labanotation Labanotation (the grammatically correct form "Labannotation" or "Laban notation" is uncommon) is a system for analyzing and recording human movement. The inventor was Rudolf von Laban (1879-1958), a central figure in European modern dance, who ...

permits a graphical representation of human bodily movements * Eshkol-Wachman Movement Notation permits a graphical representation of bodily movements of other species in addition to humans, and indeed any kind of movement (e.g. aircraft aerobatics) * Juggling diagrams represent juggling patterns * Aresti aerobatic symbols provides a way to represent flight maneuvers in aerobatics

Science

Feynman diagram In theoretical physics, a Feynman diagram is a pictorial representation of the mathematical expressions describing the behavior and interaction of subatomic particles. The scheme is named after American physicist Richard Feynman, who introduce ...

s permit a graphical representation of a perturbative contribution to the transition amplitude or correlation function of a quantum mechanical or statistical field theory *

Structural formula The structural formula of a chemical compound is a graphic representation of the molecular structure (determined by structural chemistry methods), showing how the atoms are possibly arranged in the real three-dimensional space. The chemical bond ...

s are graphical representations of molecules *

Venn diagram A Venn diagram is a widely used diagram style that shows the logical relation between sets, popularized by John Venn (1834–1923) in the 1880s. The diagrams are used to teach elementary set theory, and to illustrate simple set relationships ...

s shows logical relations between a finite collection of sets. * Drakon-charts are a graphical representation of algorithms and procedural knowledge.

Other systems

Whyte notation Whyte notation is a classification method for steam locomotives, and some internal combustion locomotives and electric locomotives, by wheel arrangement. It was devised by Frederick Methvan Whyte, and came into use in the early twentieth ce ...

for classifying steam locomotives by wheel arrangement