Bracket
A bracket is either of two tall fore- or back-facing punctuation marks commonly used to isolate a segment of text or data from its surroundings. They come in four main pairs of shapes, as given in the box to the right, which also gives their names, that vary between British and American English. "Brackets", without further qualification, are in British English the... marks and in American English the... marks.
Other symbols are repurposed as brackets in specialist contexts, such as those used by linguists.
Brackets are typically deployed in symmetric pairs, and an individual bracket may be identified as a "left" or "right" bracket or, alternatively, an "opening bracket" or "closing bracket", respectively, depending on the directionality of the context.
In casual writing and in technical fields such as computing or linguistic analysis of grammar, brackets nest, with segments of bracketed material containing embedded within them other further bracketed sub-segments. The number of opening brackets matches the number of closing brackets in such cases.
Various forms of brackets are used in mathematics, with specific mathematical meanings, often for denoting specific mathematical functions and subformulas.
History
Angle brackets or chevrons ⟨ ⟩ were the earliest type of bracket to appear in written English. Erasmus coined the term lunula to refer to the round brackets or parentheses recalling the shape of the crescent moon.Most typewriters only had the left and right parentheses. Square brackets appeared with some teleprinters.
Braces first became part of a character set with the 8-bit code of the IBM 7030 Stretch.
In 1961, ASCII contained parentheses, square, and curly brackets, and also less-than and greater-than signs that could be used as angle brackets.
Typography
In English, typographers mostly prefer not to set brackets in italics, even when the enclosed text is italic. However, in other languages like German, if brackets enclose text in italics, they are usually also set in italics.Parentheses or round brackets
The marks and are parentheses in American English, and either round brackets or simply brackets in British English.In formal writing, "parentheses" is also used in British English.
Uses of ( )
Parentheses contain adjunctive material that serves to clarify or is aside from the main point.A comma before or after the material can also be used, though if the sentence contains commas for other purposes, visual confusion may result. A dash before and after the material is also sometimes used.
Parentheses may be used in formal writing to add supplementary information, such as "Senator John McCain spoke at length". They can also indicate shorthand for "either singular or plural" for nouns, e.g. "the claim". It can also be used for gender-neutral language, especially in languages with grammatical gender, e.g. "he agreed with his/her physician".
Parenthetical phrases have been used extensively in informal writing and stream of consciousness literature. Examples include the southern American author William Faulkner as well as poet E. E. Cummings.
Parentheses have historically been used where the em dash is currently used in alternatives, such as "parenthesis).
Language
A parenthesis in rhetoric and linguistics refers to the entire bracketed text, not just to the enclosing marks used. Taking as an example the sentence "Mrs. Pennyfarthing was my landlady.", the explanatory phrase between the parentheses is itself called a parenthesis. Again, the parenthesis implies that the meaning and flow of the bracketed phrase is supplemental to the rest of the text and the whole would be unchanged were the parenthesised sentences removed. The term refers to the syntax rather than the enclosure method: the same clause in the form "Mrs. PennyfarthingWhat? Yes, that was her name!was my landlady" is also a parenthesis.In phonetics, parentheses are used for indistinguishable or unidentified utterances. They are also seen for silent articulation, where the expected phonetic transcription is derived from lip-reading, and with periods to indicate silent pauses, for example or.
In some languages, such as the Nicodemus orthography for Coeur d’Alene, parentheses are used as phonemic symbols instead of punctuation.
Enumerations
An unpaired right parenthesis is often used as part of a label in an ordered list, such as this one:Accounting
Traditionally in accounting, contra amounts are placed in parentheses. A debit balance account in a series of credit balances will have parentheses and vice versa.Parentheses in mathematics
Parentheses are used in mathematical notation to indicate grouping, often inducing a different order of operations. For example: in the usual order of algebraic operations, equals 14, since the multiplication is done before the addition. However, equals 20, because the parentheses override normal precedence, causing the addition to be done first. Some authors follow the convention in mathematical equations that, when parentheses have one level of nesting, the inner pair are parentheses and the outer pair are square brackets. Example:Parentheses in programming languages
Parentheses are included in the syntaxes of many programming languages. Typically needed to denote an argument; to tell the compiler what data type the method/function needs to look for first in order to initialise. In some cases, such as in LISP, parentheses are a fundamental construct of the language. They are also often used for scoping functions and operators and for arrays. In syntax diagrams they are used for grouping, such as in extended Backus–Naur form.In Mathematica and the Wolfram language, parentheses are used to indicate groupingfor example, with pure anonymous functions.
Taxonomy
If it is desired to include the subgenus when giving the scientific name of an animal species or subspecies, the subgenus's name is provided in parentheses between the genus name and the specific epithet. For instance, Polyphylla ''alba is a way to cite the species Polyphylla alba while also mentioning that it is in the subgenus Xerasiobia. There is also a convention of citing a subgenus by enclosing it in parentheses after its genus, e.g., Polyphylla is a way to refer to the subgenus Xerasiobia within the genus Polyphylla. Parentheses are similarly used to cite a subgenus with the name of a prokaryotic species, although the International Code of Nomenclature of Prokaryotes requires the use of the abbreviation "subgen". as well, e.g., Acetobacter liquefaciens''.Chemistry
Parentheses are used in chemistry to denote a repeated substructure within a molecule, e.g. HC3 or, similarly, to indicate the stoichiometry of ionic compounds with such substructures: e.g. Ca2.This is a notation that was pioneered by Berzelius, who wanted chemical formulae to more resemble algebraic notation, with brackets enclosing groups that could be multiplied.
In chemical nomenclature, parentheses are used to distinguish structural features and multipliers for clarity, for example in the polymer poly.
Square brackets
and are square brackets in both British and American English, but are also more simply brackets in the latter.An older name for these brackets is "crotchets".
Uses of
Square brackets are often used to insert explanatory material or to mark where a passage was omitted from an original material by someone other than the original author, or to mark modifications in quotations. In transcribed interviews, sounds, responses and reactions that are not words but that can be described are set off in square brackets — "... ...".When quoted material is in any way altered, the alterations are enclosed in square brackets within the quotation to show that the quotation is not exactly as given, or to add an annotation. For example: The Plaintiff asserted his cause is just, stating,
In the original quoted sentence, the word "my" was capitalised: it has been modified in the quotation given and the change signalled with brackets. Similarly, where the quotation contained a grammatical error, the quoting author signalled that the error was in the original with "".
A bracketed ellipsis, , is often used to indicate omitted material: "I'd like to thank for their tolerance "
Bracketed comments inserted into a quote indicate where the original has been modified for clarity: "I appreciate it , but I must refuse", and "the future of psionics is in doubt". Or one can quote the original statement "I hate to do laundry" with a modification inserted: He "hate to do laundry".
Additionally, a small letter can be replaced by a capital one, when the beginning of the original printed text is being quoted in another piece of text or when the original text has been omitted for succinctness— for example, when referring to a verbose original: "To the extent that policymakers and elite opinion in general have made use of economic analysis at all, they have, as the saying goes, done so the way a drunkard uses a lamppost: for support, not illumination", can be quoted succinctly as: "olicymakers have made use of economic analysis the way a drunkard uses a lamppost: for support, not illumination." When nested parentheses are needed, brackets are sometimes used as a substitute for the inner pair of parentheses within the outer pair. When deeper levels of nesting are needed, convention is to alternate between parentheses and brackets at each level.
Alternatively, empty square brackets can also indicate omitted material, usually single letter only. The original, "Reading is also a process and it also changes you." can be rewritten in a quote as: It has been suggested that reading can "also change you".
In translated works, brackets are used to signify the same word or phrase in the original language to avoid ambiguity.
For example: He is trained in the way of the open hand .
Style and usage guides originating in the news industry of the twentieth century, such as the AP Stylebook, recommend against the use of square brackets because "They cannot be transmitted over news wires." However, this guidance has little relevance outside of the technological constraints of the industry and era.
In linguistics, phonetic transcriptions are generally enclosed within square brackets, whereas phonemic transcriptions typically use paired slashes, according to International Phonetic Alphabet rules. Pipes are often used to indicate a morphophonemic rather than phonemic representation. Other conventions are double slashes, double pipes and curly brackets.
In lexicography, square brackets usually surround the section of a dictionary entry which contains the etymology of the word the entry defines.
Proofreading
Brackets are added to the sides of text in proofreading to indicate changes in indentation:| Move left | Paradise Lost |
| Move up |
Square brackets are used to denote parts of the text that need to be checked when preparing drafts prior to finalising a document.
Law
Square brackets are used in some countries in the citation of [law reports to identify parallel citations to non-official reporters. For example:In some other countries, square brackets are used to indicate that the year is part of the citation and parentheses are used to indicate the year the judgment was given. For example:
This case is in the 1954 volume of the Appeal Cases reports, although the decision may have been given in 1953 or earlier. Compare with:
This citation reports a decision from 1954, in volume 98 of the Solicitors Journal which may be published in 1955 or later.
They often denote points that have not yet been agreed to in legal drafts and the year in which a report was made for certain case law decisions.
Square brackets in mathematics
Brackets are used in mathematics in a variety of notations, including standard notations for commutators, the floor function, the Lie bracket, equivalence classes, the Iverson bracket, and matrices.Square brackets may be used exclusively or in combination with parentheses to represent intervals as interval notation. For example, represents the set of real numbers from 0 to 5 inclusive. Both parentheses and brackets are used to denote a half-open interval; 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, but 12.0 is not included. In some European countries, the notation is also used. The endpoint adjoining the square bracket is known as closed, whereas the endpoint adjoining the parenthesis is known as open.
In group theory and ring theory, brackets denote the commutator. In group theory, the commutator is commonly defined as. In ring theory, the commutator is defined as.
Chemistry
Square brackets can also be used in chemistry to represent the concentration of a chemical substance in solution and to denote charge a Lewis structure of an ion, repeating chemical units and transition state structures, among other uses.Square brackets in programming languages
Brackets are used in many computer programming languages, primarily for array indexing. But they are also used to denote general tuples, sets and other structures, just as in mathematics. There may be several other uses as well, depending on the language at hand. In syntax diagrams they are used for optional portions, such as in extended Backus–Naur form.Double brackets ⟦ ⟧
Double brackets, , are used to indicate the semantic evaluation function in formal semantics for natural language and denotational semantics for programming languages. In the Wolfram Language, double brackets, either as iterated single brackets or ligatures are used for list indexing.The brackets stand for a function that maps a linguistic expression to its "denotation" or semantic value. In mathematics, double brackets may also be used to denote intervals of integers or, less often, the floor function. In papyrology, following the Leiden Conventions, they are used to enclose text that has been deleted in antiquity.
Lenticular brackets【】
Some East Asian languages use lenticular brackets , a combination of square brackets and round brackets. In Chinese, they are called and in Japanese, . They are used in titles and headings in both Chinese and Japanese. On the Internet, they are used to emphasise a text. In Japanese, they are most frequently seen in dictionaries for quoting Chinese characters and Sino-Japanese loanwords.Floor ⌊ ⌋ and ceiling ⌈ ⌉ corner brackets
The floor corner brackets and ceiling corner brackets are used to denote the integer floor and ceiling functions in mathematics.Quine corners ⌜⌝ and half brackets ⸤ ⸥ or ⸢ ⸣
The Quine corners and have at least two uses in mathematical logic: either as quasi-quotation, a generalisation of quotation marks, or to denote the Gödel number of the enclosed expression.Half brackets are used in English to mark added text, such as in translations: "Bill saw ⸤her⸥".
In editions of papyrological texts, half brackets, ⸤ and ⸥ or ⸢ and ⸣, enclose text which is lacking in the papyrus due to damage, but can be restored by virtue of another source, such as an ancient quotation of the text transmitted by the papyrus. For example, Callimachus Iambus 1.2 reads: "ἐκ τῶν ὅκου βοῦν κολλύ⸤βου π⸥ιπρήσκουσιν". A hole in the papyrus has obliterated "βου π", but these letters are supplied by an ancient commentary on the poem. Second intermittent sources can be between ⸢ and ⸣. Quine corners are sometimes used instead of half brackets.
Brackets with quills ⁅ ⁆
Known as "spike parentheses", and are used in Swedish bilingual dictionaries to enclose supplemental constructions.Curly brackets
and are curly brackets or braces in both American and British English.Uses of { }
Curly brackets are used by text editors to mark editorial insertions or interpolations.Braces used to be used to connect multiple lines of poetry, such as triplets in a poem of rhyming couplets, although this usage had gone out of fashion by the 19th century.
Another older use in prose was to eliminate duplication in lists and tables.
Two examples here from Charles Hutton's 19th century table of weights and measures in his A Course of Mathematics:
As an extension to the International Phonetic Alphabet, braces are used for prosodic notation.
Music
In music, they are known as "accolades" or "braces", and connect two or more lines of music that are played simultaneously.Chemistry
The use of braces in chemistry is an old notation that has long since been superseded by subscripted numbers.The chemical formula for water, H2O, was represented as.
Curly brackets in programming languages
In many programming languages, curly brackets enclose groups of statements and create a local scope. Such languages are therefore called curly bracket languages. They are also used to define structures and enumerated type in these languages.In various Unix shells, they enclose a group of strings that are used in a process known as brace expansion, where each successive string in the group is interpolated at that point in the command line to generate the command-line's final form.
The mechanism originated in the C shell and the string generation mechanism is a simple interpolation that can occur anywhere in a command line and takes no account of existing filenames.
In syntax diagrams they are used for repetition, such as in extended Backus–Naur form.
In the Z formal specification language, braces define a set.
Curly brackets in mathematics
In mathematics they delimit sets, in what is called set notation.Braces enclose either a literal list of set elements, or a rule that defines the set elements.
For example:
- defines a set containing and.
- defines a set containing elements ,, and so on where every satisfies the rule that it is greater than zero.
In ring theory, braces denote the anticommutator where is defined as.
Angle brackets
The symbols and are angle brackets in both American and British English. In computer slang, they were sometimes known as "brokets". They are also sometimes called chevrons, but chevrons normally only point upwards or downwards.The ASCII characters less-than sign and greater-than sign and are widely substituted for angle brackets. In many cases, only these substituted characters are accepted by computer programs, and the Unicode angle brackets are not recognised. The characters for "single" guillemets are also occasionally used to indicate angle brackets, and normal guillemets used when "nested" angle brackets are needed.
The angle brackets and are for mathematical use and Western languages, whereas and are double width forms for East Asian languages. The angle bracket symbols at U+2329 and U+232A are deprecated in favour of the U+3008 and U+3009 East Asian angle brackets. Unicode discourages their use for mathematics and in Western texts, because they are canonically equivalent to the CJK code points U+300n and thus likely to render as double-width symbols.
Shape
Angle brackets are larger than 'less-than' and 'greater-than' signs, which in turn are larger than guillemets.File:Angle brackets and less+greater signs and half guillemets in different fonts.svg|thumb|left|upright=3|Angle brackets, less-than/greater-than signs and single guillemets in fonts Cambria, DejaVu Serif, Andron Mega Corpus, Andika and Everson Mono
Uses of ⟨ ⟩
Angle brackets are infrequently used to denote words that are thought instead of spoken, such as:In textual criticism, and hence in many editions of pre-modern works, chevrons denote sections of the text which are illegible or otherwise lost; the editor will often insert their own reconstruction where possible within them.
In linguistics, angle brackets identify graphemes or orthography, as in "The English word is spelled."
In epigraphy, they may be used for mechanical transliterations of a text into the Latin script.
In Korean quotation marks|East Asian punctuation], angle brackets are used as quotation marks. Angle bracket symbols are part of standard Chinese, Japanese, Korean punctuation, where they generally enclose the titles of books, as: 〈 ︙ 〉 or 《 ︙ 》 for traditional vertical printing — written in vertical lines — and as 〈... 〉 or 《... 》 for horizontal printing — in horizontal.
Angle brackets in mathematics
Angle brackets are used in group theory to write group presentations, and to denote the subgroup generated by a collection of elements. In set theory, chevrons or parentheses are used to denote ordered pairs and other tuples, whereas curly brackets are used for unordered sets.Physics and mechanics
In physical sciences and statistical mechanics, angle brackets are used to denote an average over time or over another continuous parameter. For example:In mathematical physics, especially quantum mechanics, it is common to write the inner product between elements as, as a short version of, or, where is an operator. This is known as Dirac notation or bra–ket notation, to note vectors from the dual spaces of the Bra . But there are other notations used.
In continuum mechanics, chevrons may be used as Macaulay brackets.
Angle brackets in programming languages
In C++ angle brackets are used to surround arguments to templates. They are also used to surround the names of header files; this usage was inherited from and is also found in C.In the Z formal specification language, angle brackets define a sequence.
In HTML, angle brackets are used to bracket meta text. For example denotes that the following text should be displayed as bold. Pairs of meta text tags are required – much as brackets themselves are usually in pairs. The end of the bold text segment would be indicated by. This use is sometimes extended as an informal mechanism for communicating mood or tone in digital formats such as messaging, for example adding "<sighs>" at the end of a sentence.
Unicode
Representations of various kinds of brackets in Unicode and their respective List of XML and [HTML character entity references|HTML entities], that are not in the infoboxes in preceding sections, are given below.| Uses | Unicode/HTML | Sample |
| Quine corners | ⌜quasi-quotation⌝ ⌜editorial notation⌝ | |
| Quine corners | ⌜quasi-quotation⌝ ⌜editorial notation⌝ | |
| Quine corners | ⌞editorial notation⌟ | |
| Quine corners | ⌞editorial notation⌟ | |
| Brackets with quill | ⁅...⁆ | |
| Brackets with quill | ⁅...⁆ | |
| Fullwidth parentheses | ｟...｠ | |
| Fullwidth parentheses | ｟...｠ | |
| Technical/mathematical | ⎸boxed text⎹ | |
| Technical/mathematical | ⎸boxed text⎹ | |
| Technical/mathematical | ⏠ tortoise shell brackets ⏡ | |
| Technical/mathematical | ⏠ tortoise shell brackets ⏡ | |
| Technical/mathematical | ⟅...⟆ | |
| Technical/mathematical | ⟅...⟆ | |
| Technical/mathematical | ⟓pullback...pushout⟔ | |
| Technical/mathematical | ⟓pullback...pushout⟔ | |
| Technical/mathematical | ⟦...⟧ | |
| Technical/mathematical | ⟦...⟧ | |
| Technical/mathematical | ⟬white tortoise shell brackets⟭ | |
| Technical/mathematical | ⟬white tortoise shell brackets⟭ | |
| Technical/mathematical | '⦇'⦈ | |
| Technical/mathematical | '⦇'⦈ | |
| Technical/mathematical | ⦉⦊ | |
| Technical/mathematical | ⦉⦊ | |
| Technical/mathematical | ⦓inequality sign brackets⦔ | |
| Technical/mathematical | ⦓inequality sign brackets⦔ | |
| Technical/mathematical | ⦕inequality sign brackets⦖ | |
| Technical/mathematical | ⦕inequality sign brackets⦖ | |
| Technical/mathematical | ⦗black tortoise shell brackets⦘ | |
| Technical/mathematical | ⦗black tortoise shell brackets⦘ | |
| Technical/mathematical | ⧘...⧙ | |
| Technical/mathematical | ⧘...⧙ | |
| Technical/mathematical | ⧚...⧛ | |
| Technical/mathematical | ⧚...⧛ | |
| Technical/mathematical | 〚...〛 | |
| Technical/mathematical | 〚...〛 | |
| Half brackets | ⸢editorial notation⸣ | |
| Half brackets | ⸢editorial notation⸣ | |
| Half brackets | ⸤editorial notation⸥ | |
| Half brackets | ⸤editorial notation⸥ | |
| Compatibility variants for CNS 11643 | ﹙...﹚ | |
| Compatibility variants for CNS 11643 | ﹙...﹚ | |
| Compatibility variants for CNS 11643 | ﹛...﹜ | |
| Compatibility variants for CNS 11643 | ﹛...﹜ | |
| Compatibility variants for CNS 11643 | ﹝...﹞ | |
| Compatibility variants for CNS 11643 | ﹝...﹞ | |
| Dingbats | ❲light tortoise shell bracket ornament❳ | |
| Dingbats | ❲light tortoise shell bracket ornament❳ | |
| N'Ko | ||
| N'Ko | ||
| Ogham | ᚛ᚑᚌᚐᚋ᚜ | |
| Ogham | ᚛ᚑᚌᚐᚋ᚜ | |
| Old Hungarian | ⹂ | |
| Tibetan | ༺དབུ་ཅན་༻ | |
| Tibetan | ༺དབུ་ཅན་༻ | |
| Tibetan | ༼༡༢༣༽ | |
| Tibetan | ༼༡༢༣༽ | |
| New Testament editorial marks | ⸂...⸃ | |
| New Testament editorial marks | ⸂...⸃ | |
| New Testament editorial marks | ⸄...⸅ | |
| New Testament editorial marks | ⸄...⸅ | |
| New Testament editorial marks | ⸉...⸊ | |
| New Testament editorial marks | ⸉...⸊ | |
| New Testament editorial marks | ⸌...⸍ | |
| New Testament editorial marks | ⸌...⸍ | |
| Medieval studies | ⸦crux⸧ | |
| Medieval studies | ⸦crux⸧ | |
| Indicate ellipsis in certain conventions for Japanese transliteration | ⹕optional ellipsis⹖ | |
| Indicate ellipsis in certain conventions for Japanese transliteration | ⹕optional ellipsis⹖ | |
| Indicate ellipsis in certain conventions for Japanese transliteration | ⹗obligatory ellipsis⹘ | |
| Indicate ellipsis in certain conventions for Japanese transliteration | ⹗obligatory ellipsis⹘ | |
| Quotation | 〔...〕 | |
| Quotation | 〔...〕 | |
| Quotation | 〖...〗 | |
| Quotation | 〖...〗 | |
| Quotation | 〘...〙 | |
| Quotation | 〘...〙 | |
| Quotation | 〝...〞 | |
| Quotation | 〝...〞 | |
| Quotation | ｢ｶﾀｶﾅ｣ | |
| Quotation | ｢ｶﾀｶﾅ｣ | |
| Quotation | 「表題」 | |
| Quotation | 「表題」 | |
| Quotation | 『表題』 | |
| Quotation | 『表題』 | |
| Quotation | 【表題】 | |
| Quotation | 【表題】 | |
| Vertical bracket presentation forms | ︗︙︙︘ | |
| Vertical bracket presentation forms | ︗︙︙︘ | |
| Vertical bracket presentation forms | ︵︙︙︶ | |
| Vertical bracket presentation forms | ︵︙︙︶ | |
| Vertical bracket presentation forms | ︷︙︙︸ | |
| Vertical bracket presentation forms | ︷︙︙︸ | |
| Vertical bracket presentation forms | ︹︙︙︺ | |
| Vertical bracket presentation forms | ︹︙︙︺ | |
| Vertical bracket presentation forms | ︻︙︙︼ | |
| Vertical bracket presentation forms | ︻︙︙︼ | |
| Vertical bracket presentation forms | ︽︙︙︾ | |
| Vertical bracket presentation forms | ︽︙︙︾ | |
| Vertical bracket presentation forms | ︿︙︙﹀ | |
| Vertical bracket presentation forms | ︿︙︙﹀ | |
| Vertical bracket presentation forms | ﹁︙︙﹂ | |
| Vertical bracket presentation forms | ﹁︙︙﹂ | |
| Vertical bracket presentation forms | ﹃︙︙﹄ | |
| Vertical bracket presentation forms | ﹃︙︙﹄ | |
| Vertical bracket presentation forms | ﹇︙︙﹈ | |
| Vertical bracket presentation forms | ﹇︙︙﹈ |