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Brackets are punctuation marks, used in pairs to set apart or interject text within other text. Types of brackets include parentheses or round brackets ( ), box brackets or square brackets ^*, curly brackets or braces { }, and angle brackets . All these forms may be used according to typographical conventions that may vary from publication to publication and may vary even more from language to language. Some typical uses in English texts follow.

Usage

In addition to referring to the class of all types of brackets, the unqualified word "bracket" is most commonly used to refer to a specific type of bracket. In modern American usage, this is usually the square bracket, whereas in modern British usage it is usually the parenthesis.

In fact, in American usage, parentheses are usually considered separately from other brackets, and calling them "brackets" at all is unusual, even though they serve a similar function.

Types of brackets

Parentheses ( )

Parentheses (the singular is parenthesis, with an i) – sometimes called round brackets, curved brackets or just brackets; or, colloquially, parens, or fingernails – are used to contain parenthetical (or optional, additional) material in a sentence that could be removed without destroying the meaning of the main text.

John Lennard (in "The exploitation of parentheses in English printed verse") usefully coined the term lunula to refer specifically to the opening curved bracket, the closing curved bracket and the textual contents between.

In formal writing, parentheses may be used to add supplementary information, such as "Sen. Kennedy (D., Massachusetts) spoke at length."

In literature and informal writing, parenthetical phrases have been used extensively in stream of consciousness literature. Of particular note is the great southern American author William Faulkner, whose use of parenthetical constructions was legendary, effective, and (at times) frustrating. See Absalom, Absalom and the Quentin section of The Sound and the Fury for the best known examples. In most writing, overuse of parentheses is usually a sign of a badly structured text.

Historically, parentheses have been used in place of where the solidus is modernly used—that is, in order to depict alternatives, such as "parenthesis)(parentheses". Examples of this usage can be seen in editions of Fowler’s.

Parentheses may also be nested (with one set inside another set (this is not commonly used in formal writing)). Sometimes square brackets will be used for the inner set of parentheses (in other words, a secondary phrase in parentheses example, this one).

Any punctuation inside parentheses or other brackets is independent from the rest of the text: "Mrs. Pennyfarthing (What? Yes, that was her name!) was my landlady". In this usage, the explanatory text in the parentheses is a parenthesis.

In mathematics, parentheses are used to signify a different precedence of operators. For example, 2 + 3 × 4 would be 14, since the multiplication is done before the addition. On the other hand, (2 + 3) × 4 is 20, because the parentheses override normal precedence, causing the addition to be done first. They are also used to set apart the arguments to mathematical functions. For example, f(x) is the function f applied to the variable x. In the coordinate system, parentheses are used to denote a set of coordinates. For example, (4,7) may represent the point located at 4 on the x-axis and 7 on the y-axis. Parentheses can also represent multiplication, as in the instance of 2 (3) = 6.

Box brackets or square brackets

Square brackets are used to enclose explanatory or missing material, especially in quoted text. For example, "I appreciate it [the honor, but I must refuse". Or, "the future of psionics definition is in doubt".

The bracketed expression sic (Latin for "thus") is used to indicate errors that are "thus in the original"; a bracketed ellipsis is often used to indicate deleted material; bracketed comments are used to indicate when original text has been modified for clarity: "I'd like to thank ^*" target="_blank" >for their love, tolerance [… and assistance added".

Square brackets are also sometimes used as parentheses within parentheses (secondary parentheses mentioned earlier).

With the International Phonetic Alphabet, square brackets are used to indicate a phonetic transcription (as opposed to a phonemic one).

In chemistry, square brackets can also be used to represent the concentration of a chemical substance, or to denote a complex ion.

In proofreading, square brackets (called move-left symbols or move right symbols) are added to the sides of text to indicate changes in indentation:

Move left	[To Fate I sue, of other means bereft, the only refuge for the wretched left.
Center	]Paradise Lost[
Move up

Curly brackets or braces { }

Curly brackets (so-called in British English; North American English prefers braces) are sometimes used in prose to indicate a series of equal choices: "Select your animal {goat, sheep, cow, horse} and follow me". They are used in specialized ways in poetry and music (to mark repeats or joined lines). In mathematics they are used to delimit sets.

Presumably due to the similarity of the words brace and bracket (although they do not share an etymology), many people casually treat brace as a synonym for bracket. Therefore, when it is necessary to avoid any possibility of confusion, such as in computer programming, it may be best to use the term curly bracket rather than brace. However, general usage in North American English favors the latter form. The term curly braces is redundant since no other type of brace exists. Indian programmers often use the name "flower bracket".

In computer programming, curly brackets sometimes denote the beginning and ending of a sequence of statements or define a scope.

Angle brackets or chevrons

Angle brackets () are often used to enclose highlighted material. Some dictionaries use angle brackets to enclose short excerpts illustrating the usage of words. True angle brackets are not available on a typical computer keyboard, so the "less than" and "greater than" symbols are used instead (<, >). These are often loosely referred to as angle brackets when used in this way. For example, the symbols < and > are often used to set apart URLs in text, such as "I found it on Example.com ".

Angle brackets are used in mathematics and logic to delimit ordered n-tuples. They are used in physical sciences to denote an average over time or another continuous parameter. For example,

$\backslash langle\; V(t)^2\; \backslash rangle\; =\; \backslash lim\_\{T\backslash to\backslash infty\}\; \backslash frac\{1\}\{T\}\backslash int\_\{-T/2\}^\{T/2\}\; V(t)^2\{\backslash rm\{d\}\}t$

In linguistics, angle brackets are used to indicate orthography, as in "The English word is spelled ."

In textual criticism, and hence in many editions of poorly transmitted works, angle brackets denote sections of the text which are illegible or otherwise lost; the editor will often insert their own reconstruction where possible within them.

Single and double angle brackets () or pairs of the appropriate comparison operators (<<, >>) are sometimes used instead of guillemets when the proper glyphs are not available.

The mathematical or logical symbols for greater-than (>) and less-than (<), when used as such, are not punctuation marks.

Chevrons are part of standard Chinese, Japanese, and Korean punctuation, where they generally enclose the titles of books: and or and for traditional vertical printing, and and or and for horizontal printing.

In comic books, angle brackets are often used to mark dialogue that has notionally been translated from another language.

In computing

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• Opening and closing parentheses correspond to ASCII and Unicode characters 40 and 41, or 0x0028 and 0x0029, respectively.
• For square brackets corresponding values are 91 and 93, or 0x005B and 0x005D.
• For braces, 123 and 125, or 0x007B and 0x007D.
• True angle brackets are available in Unicode at code points 9001 and 9002, or 0x2329 and 0x232A. The less than and greater than symbols can be found in both Unicode and ASCII at code points 60 and 62, or 0x003C and 0x003E.

Also, in many computer languages:

• "(" and ")" are used to contain the arguments to functions: substring($val,10,1). Parentheses are so ubiquitous in the Lisp programming language that the name is said to be an acronym for "Lots of Irritating Superfluous Parentheses". They may also be used to indicate the start and end of lists.
• "and "" are used to define the number of elements in an array, or reference one of those elements: $queueAs a generalisation of this usage, many programming languages including C++, Ruby and Python allow the notation hash[key to denote looking up a value in an associative array. In MediaWiki's syntax, a double square-bracket set is used to make a wikilink to the term defined inside: Bracket. In most regular expression syntaxes square brackets are used to denote a character class: a series of possible characters to choose from.
• "{" and "}" are used to define the beginning and ending of blocks of code or define the initial contents of an array. To complicate things, in the Pascal programming language, "{" and "}" define the beginning and ending of comments. Languages which use the former convention are said to belong to the curly brace family of programming languages.
• "<" and ">" are used in SGML (and other formats based on SGML, such as HTML and XML), to enclose code tags: <div>, and in the languages Java, C++ and C# to delimit generic arguments.

Layout rules

In normal text an opening bracket is not put at the end of a line, and a closing bracket not at the beginning. However, in computer code this is often done to aid readability. For example, a bracketed list of items separated by semi-colons may be written with the brackets on separate lines, and the items, followed by the semicolon, each on one line.

For example, the CSS code:

H1 { font-weight: bold; font-size: 12pt; line-height: 14pt }

may also be written:

H1 { font-weight: bold; font-size: 12pt; line-height: 14pt }

A superfluous semicolon may be added after the last item for uniformity of the item lines.

See: Indent style

In mathematics

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In addition to the use of parentheses to specify the order of operations, both parentheses and square brackets can also be used to denote an interval. The notation [a, c) is used to indicate an interval from a to c that is inclusive of a but exclusive of c. That is, [5, 12) would be the set of all real numbers between 5 and 12, including 5 but except 12. The numbers may come as close as they like to 12, including 11.999 and so forth (with any finite number of 9s), but 12.0 is not included. In Europe, the notation [5,12[ is also used for this.

The endpoint adjoining the square bracket is known as closed, while the endpoint adjoining the parenthesis is known as open. If both types of brackets are the same, the entire interval may be referred to as closed or open as appropriate. Whenever infinity or negative infinity is used as an endpoint, it is always considered open and adjoined to a parenthesis.

This is used in mathematical notation, and appears in some computer programming languages. See the article Interval (mathematics) for a more complete treatment of the subject.

In quantum mechanics, angle brackets are also used as part of Dirac's formalism, bra-ket notation, to note vectors from the dual spaces of the Bra A| and the Ket |B. In statistical mechanics, angle brackets denote ensemble or time average.

In group theory and ring theory, square brackets are used to denote the commutator. In group theory, the commutator is commonly defined as g⁻¹h⁻¹gh. In ring theory, the commutator [a,b is defined as ab − ba. Furthermore, in ring theory, braces are used to denote the anticommutator where {a,b} is defined as ab + ba.

Various notations, like the vinculum have a similar effect to brackets in specifying order of operations, or otherwise grouping several characters together for a common purpose.

In the Z formal specification language, curly braces define a set and angle brackets define a sequence.

In sports

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• Tournament brackets, such as those used in sports tournaments (tennis tournaments, 9-ball tournaments, or March Madness and other NCAA tournaments).

In law

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Brackets are used in the citation of law reports to identify whether the report series is sorted by volume number - in which case round brackets are used - or by year - in which case square brackets are used. For example: (1983) 158 CLR 1 or ^* 2 All ER 153.

In mechanics and structures

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A bracket may be an inverted "L" shape, such as is usually used to hold up a shelf, or a rafter extension and its diagonal brace supporting an overhanging roof over a gable. Decorative brackets used in furniture and mantlepieces are called corbels.

Reference

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• Turnbull et al., The Graphics of Communication, Holt, New York: 1964 states that what are depicted as square brackets above are called braces and curly brackets are called brackets. This was the terminology in US printing prior to computers.

See also

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• Tax bracket
• Bra-ket notation
• Emoticon
• Japanese typographic symbols
• List of songs with brackets in their titles

Punctuation | Mathematical notation | Typography

Parèntesi | Parentes | Klammer (Zeichen) | Paréntesis | Krampo | Parentesiak | Parenthèse | סוגריים | Haakje | 括弧 | Parentes | Скобки | Sulkeet | Parentes | 括号