Abracket is either of two tall fore- or back-facingpunctuation marks commonly used to isolate a segment of text or data from its surroundings.[3] They come in four main pairs of shapes, as given in the box to the right, which also gives their names, that vary betweenBritish andAmerican English.[1] "Brackets", without further qualification, are in British English the(...) marks and in American English the[...] marks.[1][3]
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",[5] respectively, depending on thedirectionality of the context.
In casual writing and in technical fields such as computing or linguistic analysis ofgrammar, bracketsnest, with segments of bracketed material containing embedded within them other further bracketed sub-segments.[3] The number of opening brackets matches the number of closing brackets in such cases.[3]
In English,typographers mostly prefer not to set brackets initalics, even when the enclosed text is italic.[8] However, in other languages likeGerman, if brackets enclose text in italics, they are usually also set in italics.[9]
( and) areparentheses/pəˈrɛnθɪsiːz/ (singularparenthesis/pəˈrɛnθɪsɪs/) in American English, and eitherround brackets or simplybrackets in British English.[1][4]They are also known as "parens"/pəˈrɛnz/, "circle brackets", or "smooth brackets".
In formal writing, "parentheses" is also used in British English.[citation needed]
Parentheses containadjunctive material that serves to clarify (in the manner of agloss) or is aside from the main point.[21]
A comma before or after the material can also be used, though if the sentence contains commas for other purposes, visual confusion may result. Adash 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 (R - Arizona) spoke at length". They can also indicate shorthand for "either singular or plural" for nouns, e.g. "the claim(s)". It can also be used forgender-neutral language, especially in languages withgrammatical gender, e.g. "(s)he agreed with his/her physician" (the slash in the second instance, as one alternative is replacing the other, not adding to it).
Parentheses have historically been used where theem dash is currently used in alternatives, such as "parenthesis)(parentheses". Examples of this usage can be seen in editions ofFowler's Dictionary of Modern English Usage.
Parentheses may be nested (generally 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 parenthetical sentence]).
Aparenthesis in rhetoric andlinguistics refers to the entire bracketed text, not just to the enclosing marks used (so all the text in this set of round brackets may be described as "a parenthesis").[22] Taking as an example the sentence "Mrs. Pennyfarthing (What? Yes, that was her name!) 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 parenthesized sentences removed. The term refers to the syntax rather than the enclosure method: the same clause in the form "Mrs. Pennyfarthing – What? Yes, that was her name! – was my landlady" is also a parenthesis.[23] (In non-specialist usage, the term "parenthetical phrase" is more widely understood.[24])
Inphonetics, parentheses are used for indistinguishable[25] or unidentified utterances. They are also seen for silent articulation (mouthing),[26] where the expected phonetic transcription is derived from lip-reading, and with periods to indicate silent pauses, for example(...) or(2sec).
Traditionally inaccounting, contra amounts are placed in parentheses. A debit balance account in a series of credit balances will have parenthesis and vice versa.
Parentheses are used inmathematical notation to indicate grouping, often inducing a differentorder of operations. For example: in the usual order of algebraic operations,4 × 3 + 2 equals 14, since themultiplication is done before theaddition. However,4 × (3 + 2) 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 are included in the syntaxes of manyprogramming 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 inLISP, parentheses are a fundamental construct of the language. They are also often used for scoping functions and operators and for arrays. Insyntax diagrams they are used for grouping, such as inextended Backus–Naur form.
In Mathematica and the Wolfram language, parentheses are used to indicate grouping – for example, with pure anonymous functions.
If it is desired to include thesubgenus when giving thescientific name of an animal species orsubspecies, the subgenus's name is provided in parentheses between thegenus name and thespecific epithet.[27] For instance,Polyphylla (Xerasiobia)alba is a way to cite the speciesPolyphylla alba while also mentioning that it is in the subgenusXerasiobia.[28] There is also a convention of citing a subgenus by enclosing it in parentheses after its genus, e.g.,Polyphylla (Xerasiobia) is a way to refer to the subgenusXerasiobia within the genusPolyphylla.[29] Parentheses are similarly used to cite a subgenus with the name of aprokaryotic species, although theInternational Code of Nomenclature of Prokaryotes (ICNP) requires the use of the abbreviation "subgen". as well, e.g.,Acetobacter (subgen.Gluconoacetobacter)liquefaciens.[30]
Parentheses are used inchemistry to denote a repeated substructure within a molecule, e.g. HC(CH3)3 (isobutane) or, similarly, to indicate the stoichiometry of ionic compounds with such substructures: e.g. Ca(NO3)2 (calcium nitrate).
This is a notation that was pioneered byBerzelius, who wanted chemical formulae to more resemble algebraic notation, with brackets enclosing groups that could be multiplied (e.g. in 3(AlO2 + 2SO3) the 3 multiplies everything within the parentheses).[31][32]
[ and] aresquare brackets in both British and American English, but are also more simplybrackets in the latter.[1][3]An older name for these brackets is "crotchets".[35]
Square brackets are often used to insert explanatory material or to mark where a [word or] passage was omitted from an original material by someone other than the original author, or to mark modifications in quotations.[36] In transcribed interviews, sounds, responses and reactions that are not words but that can be described are set off in square brackets — "... [laughs] ...".
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 anannotation.[37] For example:The Plaintiff asserted his cause is just, stating,
In the original quoted sentence, the word "my" was capitalized: it has been modified in the quotation given and the change signalled with brackets. Similarly, where the quotation contained a grammatical error (is/are), the quoting author signalled that the error was in the original with "[sic]" (Latin for 'thus').
A bracketedellipsis, [...], is often used to indicate omitted material: "I'd like to thank [several unimportant people] for their tolerance [...]"[38]Bracketed comments inserted into a quote indicate where the original has been modified for clarity: "I appreciate it [the honor], but I must refuse", and "the future of psionics [see definition] is in doubt". Or one can quote the original statement "I hate to do laundry" with a (sometimes grammatical) modification inserted: He "hate[s] 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 averbose 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: "[P]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.[39] 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".[40]
In translated works, brackets are used to signify the same word or phrase in the original language to avoid ambiguity.[41]For example:He is trained in the way of the open hand [karate].
In linguistics,phonetic transcriptions are generally enclosed within square brackets,[43] whereasphonemic transcriptions typically use pairedslashes, according toInternational Phonetic Alphabet rules. Pipes (| |) are often used to indicate amorphophonemic rather than phonemic representation. Other conventions are double slashes (⫽ ⫽), double pipes (‖ ‖) and curly brackets ({ }).
Inlexicography, square brackets usually surround the section of a dictionary entry which contains theetymology of the word the entry defines.
In some other countries (such asEngland and Wales), 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:
National Coal Board v England [1954] AC 403
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:
(1954) 98 Sol Jo 176
This citation reports a decision from 1954, in volume 98 of theSolicitors 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 certaincase law decisions.
Square brackets may be used exclusively or in combination with parentheses to representintervals asinterval notation.[44] For example,[0,5] represents the set of real numbers from 0 to 5 inclusive. Both parentheses and brackets are used to denote ahalf-open interval;[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, but 12.0 is not included. In some European countries, the notation[5, 12[ is also used.[45][46] The endpoint adjoining the square bracket is known asclosed, whereas the endpoint adjoining the parenthesis is known asopen.[44]
Ingroup theory andring theory, brackets denote thecommutator. In group theory, the commutator[g, h] is commonly defined asg −1h −1gh. In ring theory, the commutator[a, b] is defined asab −ba.
Square brackets can also be used inchemistry to represent theconcentration of achemical substance in solution and to denote charge a Lewis structure of an ion (particularly distributed charge in acomplex ion), repeating chemical units (particularly in polymers) and transition state structures, among other uses.
Brackets are used in many computerprogramming languages, primarily forarray 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. Insyntax diagrams they are used for optional portions, such as inextended Backus–Naur form.
Double brackets (or white square brackets orScott brackets), ⟦ ⟧, are used to indicate thesemantic evaluation function informal semantics for natural language anddenotational semantics for programming languages.[47][48] In theWolfram Language, double brackets, either as iterated single brackets ([[) or ligatures (〚) are used forlist indexing.[49]
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 denoteintervals of integers or, less often, thefloor function. In papyrology, following theLeiden Conventions, they are used to enclose text that has been deleted in antiquity.[50]
SomeEast Asian languages use lenticular brackets【】, a combination of square brackets and round brackets called方頭括號 (fāngtóu kuòhào) inChinese and隅付き括弧 (sumitsuki kakko) inJapanese. They are used in titles and headings in both Chinese[51] and Japanese. On the Internet, they are used to emphasize a text. In Japanese, they are most frequently seen in dictionaries for quoting Chinese characters and Sino-Japanese loanwords.
Half brackets are used in English to mark added text, such as in translations: "Bill saw ⸤her⸥".
In editions ofpapyrological 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.[52] For example,CallimachusIambus 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.[15]
An example of curly brackets used to group sentences together
Curly brackets are used by text editors to mark editorial insertions[54] or interpolations.[55]
Braces used to be used to connect multiple lines of poetry, such as triplets in a poem of rhymingcouplets,[56] although this usage had gone out of fashion by the 19th century.[57][58]
Another older use in prose was to eliminate duplication in lists and tables.[58]Two examples here fromCharles Hutton's 19th century table of weights and measures in hisA Course of Mathematics:
The use of braces in chemistry is an old notation that has long since been superseded by subscripted numbers.[31]The chemical formula for water, H2O, was represented as.[31]
In many programming languages, curly brackets enclose groups ofstatements and create a localscope. Such languages (C, C#, C++ and many others) are therefore calledcurly bracket languages.[62] They are also used to define structures andenumerated type in these languages.
In variousUnix shells, they enclose a group of strings that are used in a process known asbrace 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.[63]The mechanism originated in theC 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.[64]
Inmathematics they delimitsets, in what is calledset notation.[65]Braces enclose either a literal list of set elements, or a rule that defines the set elements.[65]For example:
S = {x | x > 0} defines a setS containing elements (implied to be numbers)x0,x1, and so on where everyxn satisfies the rule that it is greater than zero.[65]
They are often also used to denote thePoisson bracket between two quantities.
U+276E❮HEAVY LEFT-POINTING ANGLE QUOTATION MARK ORNAMENT
U+276F❯HEAVY RIGHT-POINTING ANGLE QUOTATION MARK ORNAMENT
The symbols⟨ and⟩ areangle brackets in both American and British English.[1][3] In (largely archaic)computer slang, they were sometimes known as "brokets".[66]
Strictly speaking they are distinct from V-shapedchevrons, as they have (where the typography permits it) a broader span than chevrons,[67] although when printed often no visual distinction is made.[4]
The ASCII less-than and greater-than characters< and> are often used for angle brackets. In many cases, only those characters are accepted by computer programs, and the Unicode angle brackets are not recognized (for instance, inHTML tags). The characters for "single"guillemets (‹ and›) are also often used, and sometimes normal guillemets (« and») when nested angle brackets are needed.
The angle brackets or chevronsU+27E8⟨MATHEMATICAL LEFT ANGLE BRACKET andU+27E9⟩MATHEMATICAL RIGHT ANGLE BRACKET are for mathematical use and Western languages, whereasU+3008〈LEFT ANGLE BRACKET andU+3009〉RIGHT ANGLE BRACKET are for East Asian languages. The chevrons 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,[15] because they are canonically equivalent to the CJK code points U+300n and thus likely to render as double-width symbols. Theless-than andgreater-than symbols are often used as replacements for chevrons.
^abcd⟨ and ⟩ were tied to the deprecated symbols U+2329 and U+232A in HTML4 and MathML2, but are being migrated to U+27E8 and U+27E9 for HTML5 and MathML3, as defined inXML Entity Definitions for Characters (Archived 27 January 2013 at theWayback Machine).
Angle brackets are infrequently used to denotewords that are thought instead of spoken, such as:
⟨What an unusual flower!⟩
Intextual 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.[68]
Incomic books, chevrons are often used to mark dialogue that has been translated notionally from another language; in other words, if a character is speaking another language, instead of writing in the other language and providing a translation, one writes the translated text within chevrons. Since no foreign language is actually written, this is onlynotionally translated.[citation needed]
Inepigraphy, they may be used for mechanical transliterations of a text into the Latin script.[70]
InEast Asian punctuation, angle brackets are used asquotation marks. Chevron-like symbols are part of standardChinese,Japanese and – less frequently – Korean punctuation, where they generally enclose the titles of books, as:〈 ︙ 〉 or《 ︙ 》 for traditionalvertical printing — written in vertical lines — and as 〈 ... 〉 or 《 ... 》 forhorizontal printing — in horizontal.
In physical sciences and statistical mechanics, angle brackets are used to denote an average (expected value) over time or over another continuous parameter. For example:
In mathematical physics, especiallyquantum mechanics, it is common to write theinner product between elements as⟨a|b⟩, as a short version of⟨a|·|b⟩, or⟨a|Ô|b⟩, whereÔ is anoperator. This is known asDirac notation orbra–ket notation, to note vectors from thedual spaces of the Bra ⟨A| and the Ket |B⟩. But there areother notations used.
InC++ angle brackets (actually less-than and greater-than) are used to surround arguments totemplates. They are also used to surround the names ofheader files; this usage was inherited from and is also found inC.
InHTML, angle brackets (actually 'greater than' and 'less than' symbols) are used to bracket meta text. For example<b> 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</b>. 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.
Representations of various kinds of brackets inUnicode and their respectiveHTML entities, that are not in the infoboxes in preceding sections, are given below.
Unicode and HTML encodings for various bracket characters
U+FE17︗PRESENTATION FORM FOR VERTICAL LEFT WHITE LENTICULAR BRACKET
︗︙︙︘
U+FE18︘PRESENTATION FORM FOR VERTICAL RIGHT WHITE LENTICULAR BRACKET[c]
U+FE35︵PRESENTATION FORM FOR VERTICAL LEFT PARENTHESIS
︵︙︙︶
U+FE36︶PRESENTATION FORM FOR VERTICAL RIGHT PARENTHESIS
U+FE37︷PRESENTATION FORM FOR VERTICAL LEFT CURLY BRACKET
︷︙︙︸
U+FE38︸PRESENTATION FORM FOR VERTICAL RIGHT CURLY BRACKET
U+FE39︹PRESENTATION FORM FOR VERTICAL LEFT TORTOISE SHELL BRACKET
︹︙︙︺
U+FE3A︺PRESENTATION FORM FOR VERTICAL RIGHT TORTOISE SHELL BRACKET
U+FE3B︻PRESENTATION FORM FOR VERTICAL LEFT BLACK LENTICULAR BRACKET
︻︙︙︼
U+FE3C︼PRESENTATION FORM FOR VERTICAL RIGHT BLACK LENTICULAR BRACKET
U+FE3D︽PRESENTATION FORM FOR VERTICAL LEFT DOUBLE ANGLE BRACKET
︽︙︙︾
U+FE3E︾PRESENTATION FORM FOR VERTICAL RIGHT DOUBLE ANGLE BRACKET
U+FE3F︿PRESENTATION FORM FOR VERTICAL LEFT ANGLE BRACKET
︿︙︙﹀
U+FE40﹀PRESENTATION FORM FOR VERTICAL RIGHT ANGLE BRACKET
U+FE41﹁PRESENTATION FORM FOR VERTICAL LEFT CORNER BRACKET
﹁︙︙﹂
U+FE42﹂PRESENTATION FORM FOR VERTICAL RIGHT CORNER BRACKET
U+FE43﹃PRESENTATION FORM FOR VERTICAL LEFT WHITE CORNER BRACKET
﹃︙︙﹄
U+FE44﹄PRESENTATION FORM FOR VERTICAL RIGHT WHITE CORNER BRACKET
U+FE47﹇PRESENTATION FORM FOR VERTICAL LEFT SQUARE BRACKET
﹇︙︙﹈
U+FE48﹈PRESENTATION FORM FOR VERTICAL RIGHT SQUARE BRACKET
^This is fullwidth version ofU+2033″DOUBLE PRIME. In vertical texts,U+301F〟LOW DOUBLE PRIME QUOTATION MARK is preferred.
^These characters are not used in typical documents. Instead the respective horizontal characters are used and the character that is rendered depends on thewriting direction.
^The original name of this character is "Presentation Form For Vertical Right White Lenticular Brakcet [sic]". Since Unicode character names cannot be changed, this character has the corrected name as analias.
^"Unicode Bidirectional Algorithm".Unicode Technical Reports. Unicode Consortium. § 3.1.3 Paired Brackets.Archived from the original on 3 October 2018. Retrieved24 April 2018.
^"Names of subgenera".International Code of Zoological Nomenclature (4th ed.). International Commission on Zoological Nomenclature. 2012.Archived from the original on 7 June 2021. Retrieved6 June 2021.
^Wilson, Kenneth G. (1993)."Brackets (Square, Angle)".The Columbia Guide to Standard American English. Columbia University Press. Archived fromthe original on 24 May 2008 – via Bartleby.com.
^Dowty, D., Wall, R. and Peters, S.: 1981, Introduction to Montague semantics, Springer.
^Scott, D.; Strachey, C. (1971).Toward a Mathematical Semantics for Computer Languages. Oxford University Computing Laboratory, Programming Research Group.
^"Part, Wolfram Language function".Reference.Wolfram.com. Wolfram Research. 2014 [1988]. Archived fromthe original on 31 March 2023.In StandardForm and InputForm,expr[[spec]] can be input asexpr〚spec〛.
^Hefferon, Jim.Linear algebra(PDF) (Third ed.). Saint Michael's College. p. 121.Archived(PDF) from the original on 3 December 2020. Retrieved26 March 2021.
Pointon, Graham; Clark, Stewart (2014). "Punctuation Guide".Words: A User's Guide. Routledge.ISBN9781317864295.
Peters, Pam (2007).The Cambridge Guide to Australian English Usage (2nd ed.). Cambridge University Press.ISBN9781139465212.
Watts, Henry (1877). "Notation".A Dictionary of Chemistry and the Allied Branches of Other Sciences. Vol. 4. Longmans, Green, and Company.
Newham, Cameron; Rosenblatt, Bill (1998).Learning the Bash Shell. O'Reilly Media.ISBN9781565923478.
Sobell, Mark G.; Seebach, Peter (2005).A Practical Guide to UNIX for Mac OS X Users. Prentice Hall Professional.ISBN9780321629982.
Biggs, Norman (2002). "Set notation".Discrete Mathematics. OUP Oxford.ISBN9780198507178.
Ihde, Aaron J. (1984).The Development of Modern Chemistry. Dover Books on Chemistry. Courier Corporation.ISBN9780486642352.
Achatz, Thomas; Anderson, John G. (2005). McKenzie, Kathleen (ed.).Technical Shop Mathematics. Industrial Press.ISBN9780831130862.
Wilson, John (1850).Treatise on English Punctuation (2nd ed.). Boston: Published by the author.
Robertson, Joseph (1785).An Essay on Punctuation. London: J. Walter.
Hutton, Charles (1836). Gregory, Olinthus (ed.).A Course of Mathematics. Vol. 1 (11th ed.). London: Longman, Rees.
Lennard, John (1991).But I Digress: The Exploitation of Parentheses in English Printed Verse. Oxford: Clarendon Press.ISBN0198112475.
Turnbull, Arthur T.; Baird, Russell N. (1964).The Graphics of Communication: Typography, Layout, Design. New York: Holt, Rinehart and Winston. States that what are depicted as brackets above are called braces and braces are called brackets. This was the terminology in US printing prior to computers.
