In linguistics and semiotics, a notation is a

system A system is a group of Interaction, 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 (systems), environment, is described by its boundaries, ...

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 conc ...

character Character or Characters may refer to: Arts, entertainment, and media Literature * ''Character'' (novel), a 1936 Dutch novel by Ferdinand Bordewijk * ''Characters'' (Theophrastus), a classical Greek set of character sketches attributed to The ...

s and abbreviated expressions, used (for example) in artistic and scientific disciplines to represent technical facts and quantities by

convention Convention may refer to: * Convention (norm), a custom or tradition, a standard of presentation or conduct ** Treaty, an agreement in international law * Convention (meeting), meeting of a (usually large) group of individuals and/or companies in a ...

. Therefore, a notation is a collection of related symbols that are each given an arbitrary meaning, created to facilitate structured communication within a domain knowledge or

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 grass ...

. 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 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 ...

, physics,

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 ...

and biology, but can also be seen in areas like

business Business is the practice of making one's living or making money by producing or Trade, buying and selling Product (business), products (such as goods and Service (economics), services). It is also "any activity or enterprise entered into for pr ...

, economics and music.

Written communication

Writing systems

* Phonographic writing systems, by definition, use symbols to represent components of auditory language, i.e.

speech Speech is a human vocal communication using language. Each language uses Phonetics, 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 ...

, which in turn refers to things or ideas. The two main kinds of phonographic notational system are the alphabet 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 graphemes) with sound (or phonemes), and are therefore considered to have better phonemic orthography. * Ideographic writing, by definition, refers to things or ideas independently of their pronunciation in any language. Some ideographic systems are also pictograms 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 linguistics to distinguish written from spoken forms, etc. See .

Biology and medicine

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

Cytogenetic notation The following table summarizes symbols and abbreviations used in cytogenetics: See also *Chromosome abnormalities *Directionality (molecular biology) for 3' and 5' notation *locus (genetics) for basic notational system *International System for ...

* Energy Systems Language

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 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 it ...

is an identifier naming convention in computer programming, that represents the

type Type may refer to: Science and technology Computing * Typing, producing text via a keyboard, typewriter, etc. * Data type, collection of values used for computations. * File type * TYPE (DOS command), a command to display contents of a file. * Ty ...

or intended use of a

variable Variable may refer to: * Variable (computer science), a symbolic name associated with a value and whose associated value may be changed * Variable (mathematics), a symbol that represents a quantity in a mathematical expression, as used in many ...

with a specific pattern within its name. *

Mathematical markup languages Mathematical Markup Language (MathML) is a mathematical markup language, an application of XML for describing mathematical notations and capturing both its structure and content. It aims at integrating mathematical formulae into World Wide Web ...

are computer notations for representing mathematical formulae. * Various notations have been developed to specify regular expressions. * 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

Management

* Time and motion study symbols such as

therblig Therbligs are 18 kinds of elemental motions, used in the study of motion economy in the workplace. A workplace task is analyzed by recording each of the therblig units for a process, with the results used for optimization of manual labour by elimin ...

Mathematics

* Mathematical notation 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 in t ...

, 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 t ...

, common representations of the derivative in calculus **

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 Lan ...

, 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 and first-order predicate logic ** Ordinal notation **

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. Defining ...

, a formal notation for defining sets in set theory * Systems to represent very large numbers ** Conway chained arrow notation ** Knuth's up-arrow notation **

Steinhaus–Moser notation In mathematics, Steinhaus–Moser notation is a notation for expressing certain large numbers. It is an extension (devised by Leo Moser) of Hugo Steinhaus's polygon notation. Definitions : 20px, n in a triangle a number in a triangle means nn ...

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 systems, 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, decimal numbers. They are also used for writing numbers in other systems such as octal, and for writing identifiers ...

s ** Roman numerals ** Scientific notation for expressing large and small numbers ** Sign-value notation, 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 positional notation in base two *** Octal notation, a positional notation in base eight, used in some computers *** Decimal notation, 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 notation, an ancient numeral system in base sixty * See also Table of mathematical symbols - 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. Mathema ...

, or Dirac notation, is an alternative representation of probability distributions in quantum mechanics. * Tensor index notation 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 tensors.

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 a ...

, the common arithmetic and logical formula notation, such as "''a'' + ''b'' − ''c''". * Polish notation or "prefix notation", which places the operator before the operands (arguments), such as "+ ''a'' ''b''". * Reverse Polish notation 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 Chess notation systems are used to record either the moves made or the position of the pieces in a game of chess. Chess notation is used in chess literature, and by players keeping a record of an ongoing game. The earliest systems of notation used ...

, 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 **

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 sys ...

* Siteswap 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 fo ...

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 provides by far the most widely used system of modern musical symbols.

Dance and movement

* Benesh Movement Notation permits a graphical representation of human bodily movements * Laban Movement Analysis or Labanotation 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 diagrams 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 bondi ...

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

Other systems

* Whyte notation for classifying steam locomotives by wheel arrangement