Bracket

A clip is a sign or symbol that is used to describe a bracketing.

In the written language, it serves as punctuation marks to structure the syntactic form. A generous use of parentheses is in German typesetting considered bad, dashes, or the resolution of complex sentences are usually preferred. In other languages ​​, eg in English, brackets are used frequently.

In mathematics press clips including a precedence of arithmetic operation to be performed before others in the computing sequence from. For example, is the result of equal 5 because it performs the calculation in the parentheses first, however, is equal to 3, since the procedure is in this case from left to right. In the higher mathematics braces are also many other purposes, especially the designation of arguments of a function. Braces, brackets, and angle brackets usually have a special meaning in mathematics.

Similarly, parentheses are also used in many programming languages ​​to group several types of program elements.

In the natural sciences braces are not only mathematical calculation operations. Square brackets are used in the physics of view of the unit of a physical quantity, ie its dimension in the chemical used square brackets for the identification of concentrations. In addition, there are parentheses if constants of nature can not be accurately measured, but are estimated. To a further number is added to the constant value in parentheses. See CODATA

• 3.1 grouping parentheses in terms
• 3.2 Set braces
• 3.3 interval brackets
• 3.4 Function Arguments
• 3.5 AND brackets
• 3.6 Special operators
• 3.7 derivations

Brackets in the grammar and typography

Common are several kinds of brackets as punctuation, which are almost exclusively in pairs ( ie as opening and closing parenthesis) used; the English names differ in the UK (BE) and American (AE) English:

Before an open and after a closing parenthesis, a space is always set (unless it follows - as here - a set of characters). After an opening and before a closing parenthesis is not. ( A set point is before a closing parenthesis only when a complete set - as here -. Bracketed )

Brackets in the International Phonetic Alphabet

Brackets

The International Phonetic Alphabet (IPA ) distinguishes the left square bracket " [" and right square bracket "]".

In the IPA type the characters "[" and "]" to the beginning or end of each of the phonetic transcription; they have the IPA numbers 901 and 902, respectively ( HTML entity [= [, and ] =] ).

Curly / braces

The curly / curly brackets in the International Phonetic Alphabet to indicate the beginning or end of prosodic notation; ( HTML entities = { { and } } = ).

Brackets in mathematics

In mathematics, parentheses are also usually used in pairs, with opening and closing brackets are each mirror-symmetrical to each other. However, there are exceptions, such as interval brackets and single, not paired brackets are sometimes used.

Grouping parentheses in terms

Parentheses to group subterms and can thus alter the rank and order of calculation or are merely optical Summary of partial terms. Here usually round brackets are used:

In complex terms or if special subterms should be identified, they can be edged with square brackets.

Example:

Instead of

The size of a typographic staple is usually adapted to their hierarchical position, as in the last example.

Amount brackets

In quantities normally curly brackets are used:

Interval brackets

For intervals are different notations. The two most common are in the case of an open interval and a semi- open interval:

Instead of a semicolon, a comma to separate the interval boundaries is often used when a confusion with the decimal point.

Function arguments

Normally arguments of functions in parentheses are set, occasionally also in angle, to allow a better differentiation to group brackets ( f is a function g is a variable):

You can meet such a notation especially where complex bracketed terms appear in various functions, such as in the statistics:

AND brackets

If multiple statements are vertically grouped in a large curly bracket, it means that these are ANDed. example:

Special operators

Other brackets also pairs used are special operators or functions:

• (sometimes ) denotes the largest integer less than or equal to ( " floor function " )
• Denotes the smallest integer greater than or equal
• Refers to the amount of
• Is a notation for the average or expectation value of a quantity
• Can denote a binomial coefficients (if and are integers and ) or a matrix, this matrix can represent a vector
• Denotes the Stirling numbers of the first kind
• Denotes the Stirling numbers of the second kind
• Is a scalar or Cantor's pairing function from the individual vectors ( "Bra ") and ( " chain "); derived from the Bra- Ket notation.
• The commutator is of the two or more operators and the mathematical formalism of the quantum mechanics, where
• , The anticommutator of two operators is defined. An alternate spelling is.
• Is the Poisson bracket, a bilinear differential operator in the Hamiltonian mechanics.
• Is the short notation of the integral, see also integral calculus.
• Denotes the Falling or factorial. But confusion with the Pochhammer symbol, which is depending on the author depicted as, or.

Derivations

Higher derivatives are often characterized instead of deriving lines with an exponent in parentheses, which increases readability:

This notation is also used when the number of derivatives to be expressed even over a variable or an expression:

Brackets in programming languages

Brackets have different meanings in different programming languages. Certain meanings, however, are relatively widespread:

Parentheses:

• Determining the order of calculation in terms ( as in mathematics )
• Function arguments
• Type conversion operator (for example in C and C )
• Index array access ( for example, in BASIC)
• List education (eg in LISP and related languages ​​)
• Comment delimiters (for example, in Forth )
• Double round brackets are used by gcc for attributes.

Square brackets:

• Index array access (e.g., in C and related languages ​​)
• List operations (eg in Python, logo and some others)
• The syntactic element for introducing a lambda expression; contains possibly the Catch Clause of the lambda expression (in C 11)
• Double square brackets are used in C 11 attributes.

Braces (also called " curly brackets " ):

• Array structure and literals (C, C , Java )
• Comments ( Pascal )
• Hash access ( Perl)

Angle brackets ( only the ASCII characters < and>):

• Template arguments (eg in C , Java, version 1.5 )
• Tag delimiter (e.g., SGML, HTML, XML )

Brackets as graphic elements

Brackets, especially the parenthesis are used in emoticons.

Swell

• Punctuation mark
• Mathematical signs