Notation

The term notation can be used in several contexts. Commonly, "notation" refers to the typographical conventions or rules of symbol usage that are followed, e.g., within a book or article. Notation may refer to notation systems, meaning an interpreted system of tokens having a syntax and semantics.

Examples of this typographical conventions include

• Infix notation for representing calculations in an almost linguistic format, such as a+b-c
• Prefix notation or Polish notation, which places the operator before the operands, such as + a b
• Postfix notation or reverse Polish notation, which places the operator after the operands, such as a b +
• Numeral systems, notation for writing numbers, including
  • Positional notation, which made writing numbers more systematic than a tally method like Roman numerals
  • binary notation, a positional notation in base two
  • decimal notation, a positional notation in base ten
  • scientific notation for expressing large and small numbers
• See also Math symbols – for general tokens and their definitions.

Examples of notation systems

• In mathematics, mathematical notation is used to represent mathematical ideas, such as:
  • Conway's chained arrow, Knuth's up-arrow notation and Steinhaus polygon notation are systems to iterate exponentiation, for representing very^veryvery large numbers.
  • Cartesian Coordinate System, for representing position and other spatial concepts in analytic geometry
  • Leibnitz notation is the standard representation for Calculus
  • Big O notation, used for example in analysis to represent less significant elements of an expression, to indicate that they will be neglected
  • Z notation – a formal notation for specifying objects using Zermelo-Fraenkel set theory and first-order predicate logic
• In physics physics notation:
  • In quantum mechanics, Dirac's Bra-ket notation is another representation of probability amplititudes
  • In general relativity, for example, Tensor notation is a general way to represent a gravitational field
• In chemistry, the Lewis notation denotes chemical bonds

• Musical notation – to represent music in a musical composition
• Dance notation – to document various forms of is used to dance movement such as Labanotation, Benesh Notation, and Eshkol-Wachman notation.