Bracket

For other senses of this word, see bracket (disambiguation).

For technical reasons, :) and some similar combinations redirect here. See emoticon.

Brackets are punctuation marks used in pairs to set apart or interject text within other text. With respect to computer science, the term is sometimes said to only strictly apply to the square or box type.

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 (round bracket).

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. In more formal usage, parenthesis or parenthesised may refer to the whole bracketed text, not just to the particular punctuation marks used {so all the text in this curly bracket may be said to be parenthesised}.

It must be noted that commas must go outside of the parenthesis, unlike quotation marks.

Types of brackets

Parentheses ( )

Parentheses (the singular is parenthesis, with an i) – sometimes called round brackets, curved brackets, oval 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.

In formal writing, parentheses may be used to add supplementary information, such as "Sen. Edward Kennedy (D., Massachusetts) spoke at length." They can also indicate shorthand for "either singular or plural" for nouns—e.g., "the claim(s)".

In literature and informal writing, parenthetical phrases have been used extensively in stream of consciousness literature. Of particular note is the southern American author William Faulkner (see Absalom, Absalom! and the Quentin section of The Sound and the Fury). In most writing, overuse of parentheses is usually a sign of a badly structured text. A milder effect may be obtained by using a pair of commas as the delimiter. If the sentence contains commas for other purposes, visual confusion may result.

Historically, parentheses have been used 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 (such as this) inside another set). This is not commonly used in formal writing (though sometimes other brackets [especially square brackets] will be used for one or more inner set of parentheses [in other words, secondary {or even tertiary} phrases can be found within the main sentence]).

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. (It is most common for the parenthesised text to be within a single sentence, but not uncommon for an entire sentence, or even several sentences, of supplemental material to be in parenthesis. In this case, even the final full-stop - period - would be within the parentheses. Again, the parenthesis implies that the meaning and flow of the text as a whole would be unchanged were the parenthesised sentences removed.)

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 are also represent intervals. For example, (0,5) is the interval between 0 and 5, non-inclusive. Parentheses can also represent multiplication, as in the instance of 2 (3) = 6. Please note that in mathematic equations, if parentheses are used twice around each other, the inner pair are parentheses and the outer pair are square brackets. Ex: [5-(7+3)]+4=x. Parentheses also represent a binomial coefficient

Various brackets in Arial

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 [See 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 [several unimportant people] and my parentals [sic] for their love, tolerance […] and assistance [italics added]".

In mathematics, square brackets are used in a variety of notations, including standard notations for intervals, commutators, the Lie bracket, and the Iverson bracket.

Square brackets are also sometimes used as parentheses within parentheses (secondary parentheses [as 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 architecture, square brackets can be used to emphasize cool words, such as [metaliving] or [cityscape]. It can also be used to make the layout generally look more cool and modern.

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 favours the latter form. The term curly braces is redundant since no other type of brace exists. Indian programmers often use the name "flower bracket".

Curly brackets are often used in internet communities and through instant messaging to indicate hugging. {{{{{{{username}}}}}}}

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 <http://www.example.com/>". It may also often be found to indicate an e-mail address, such as "This photo is copyrighted by John Smith <john@smith.com>", and is the computer-readable form for such in message headers as specified by RFC 2822.

Angle brackets are used in physical sciences to denote an average over time or another continuous parameter. For example,

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

In linguistics, angle brackets are used to indicate orthography, as in "The English word /kæt/ is spelled 〈cat〉."

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 his own reconstruction where possible within them.

Single and double angle brackets (⟪, ⟫) or pairs of the appropriate comparison operators (<<, >>) are sometimes used instead of guillemets («, ») (used as quotation marks in many languages) 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.

Angle brackets can also be used to indicate an action or status (eg. <Waves> or <Offline>), particularly in online, real-time text-based discussions (instant messaging, bulletin boards, etc). (Here, asterisks can also be used to signify an action.)

In computing

• 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 0x27e8 and 0x27e9 (for mathematical use), or 0x9001 and 0x9002 (for East Asian languages), or 0x2329 and 0x232A (for "technical" use, canonically equivalent to the CJL code points 0x900x). 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 often used to define the syntactic structure of expressions, overriding operator precedence: a*(b+c) has subexpressions a and b+c, whereas a*b+c has subexpressions a*b and c.
  • are used to contain the arguments to functions: substring($val,10,1). On the other hand, in Lisp they open and close s-expressions and therefore function applications: (cons a b). In Fortran-family languages, they are also used for array references.
• "[" and "]"
  • are used to refer to array or associative array elements, and sometimes to define the number of elements in an array: queue[3].
  • 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 in some languages to define the beginning and ending of blocks of code. Languages which use this convention are said to belong to the curly brace family of programming languages. In some of these languages, they also denote array constants. On the other hand, in the Pascal programming language, "{" and "}" define the beginning and ending of comments.
• "<" and ">" are used in SGML (and its applications and variants such as HTML and XML), to enclose code tags: <div>, and in the languages Java, C++ and C# to delimit generic arguments and preprocessor directives. They are also used as operators for redirection in Unix. In this context, they are often referred to as hoinkies (singular hoinky) in order to "avoid confusion with other bracket-type operators" (Bryant and O'Hallaron 2003).

Layout styles

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

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 not 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>. Mathematicians will also commonly write <a,b> for the inner product of two vectors. In statistical mechanics, angle brackets denote ensemble or time average. Angle brackets are used in group theory to write group presentations, and to denote the subgroup generated by a collection of elements.

In group theory and ring theory, square brackets are used to denote the commutator. In group theory, the commutator [g,h] 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. The square bracket is also used to denote the Lie derivative, or more generally the Lie bracket in any Lie algebra.

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 accounting

Traditionally in accounting, negative amounts are placed in parentheses.

In law

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 [1998] 2 All ER 153.

In sports

Tournament brackets, the diagrammatic representation of the series of games played during a tournament usually leading to a single winner, are so named for their resemblance to square brackets.

History

The angle bracket was the earliest type to appear in English. Desiderius Erasmus with Brenton Wallin coined the term lunula to refer to the rounded parentheses (), recalling the round shape of the moon.

References

• Bryant, Randal E. (2003). Computer Systems: A Programmer's Perspective. Pearson Education, Inc. p. 794. ISBN 0-13-034074-X. {{cite book}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)
• Lennard, John, But I Digress: The Exploitation of Parentheses in English Printed Verse (1991) ISBN 0-19-811247-5
• 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

• Bracket notation, a text-based method of tracking changes to a document
• Emoticon
• Japanese typographic symbols