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{{about|the family of punctuation marks|other uses|Bracket (disambiguation)}}
{{redirect2|Parenthesis|parenthetical|other uses|parenthesis (disambiguation)}}
{{Redirect|( )|the Sigur Rós album|( ) (album)|other uses|( ) (disambiguation)}}
{{Punctuation marks||Brackets |variant1=( )|caption1=Round brackets or parentheses|variant2={ }|caption2=Curly brackets or braces|variant3=⟨ ⟩|caption3=Angle brackets or chevrons}}
{{Contains special characters}}
A '''bracket''' is a tall [[punctuation]] mark typically used in matched pairs within text, to set apart or interject other text. The matched pair is best described as ''opening'' and ''closing''<ref>''UAX #9: Unicode Bidirectional Algorithm'', [http://www.unicode.org/reports/tr9/#Paired_Brackets 3.1.3 Paired Brackets]</ref>. Less formally, in a left-to-right context, it may be described as ''left'' and ''right'', and in a right-to-left context, as ''right'' and ''left''.
Forms include round (also called "parentheses"), square, curly (also called "braces"), and angle brackets (also called "chevrons"); and various other pairs of symbols.
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 and in modern British usage this is usually the round bracket.
== History ==
Chevrons (< >) were the earliest type of bracket to appear in [[written English]]. [[Desiderius Erasmus]] coined the term ''lunula'' to refer to the rounded parentheses (), recalling the shape of the crescent [[moon]].<ref>Truss, Lynne. ''Eats, Shoots & Leaves'', 2003. p. 161. {{ISBN|1-59240-087-6}}.</ref>
==Names for various bracket symbols==
Some of the following names are regional or contextual.
* ( ) – parentheses, brackets (UK, Canada, New Zealand, South Africa and Australia), parens, round brackets, soft brackets, first brackets or circle brackets
* [ ] – square brackets, closed brackets, hard brackets, second brackets, crotchets,<ref>Smith, John. ''The printer’s grammar: containing a concise history of the origin of printing; Also, an examination of the superficies, gradation, and properties of The different sizes of types cast by letter founders; Various Tables of Calculation; Models of Letter Cases; Schemes for casting off Copy and Imposing; and many other Requisites for attaining a perfect Knowledge both in the Theory and Practice of the Art of Printing. With directions to authors, compilers, &c. How to Prepare Copy, and to Correct their own Proofs. Chiefly collected from SMITH’s edition. To which are added directions for pressmen, &c. The whole calculated for the Service of All who have any Concern in the Letter Press.'' p. 84.</ref> or brackets (US)
* { } – braces are "two connecting marks used in printing"; and in music "to connect staves to be performed at the same time"<ref>Concise Oxford Dictionary, 10th Edition, Oxford University Press, Great Clarendon Street, Oxford OX2 2DP, UK</ref> (UK and US), French brackets, curly brackets, definite brackets, swirly brackets, curly braces, birdie brackets, Scottish brackets, squirrelly brackets, gullwings, seagulls, squiggly brackets, twirly brackets, Tuborg brackets (DK), accolades (NL), pointy brackets, third brackets, fancy brackets, M Brace.
* ⟨ ⟩ – pointy brackets, angle brackets, triangular brackets, diamond brackets, tuples, or chevrons
* < > – inequality signs, pointy brackets, or brackets. Sometimes referred to as ''angle brackets'', in such cases as [[HTML]] markup. Occasionally known as ''broken brackets'' or ''brokets''.<ref>{{cite web|url=http://catb.org/jargon/html/B/broket.html |title=broket |publisher=Catb.org |date= |accessdate=2013-02-13}}</ref>
* ⸤ ⸥; ｢ ｣ – corner brackets
* ⟦ ⟧ – double square brackets, white square brackets
* 〔 〕 – tortoise shell brackets
* Guillemets, ‹ › and « », are sometimes referred to as chevrons or [double] angle brackets.<ref name=msterm>{{cite web |url=https://www.microsoft.com/language/en-us/Search.aspx?sString=chevron&langID=de-de |title=Terminology Search - Microsoft |website=Microsoft Language Portal - Terminology Collection|date= |author= |accessdate= 21 November 2016}}</ref>
== Typography ==
The characters ‹ › and « », known as [[guillemet]]s or ''angular quote brackets'', are actually [[quotation mark glyphs]] used in several European languages.<ref>{{cite book|title=Merriam-Webster's Manual for Writers and Editors|year=1998|publisher=[[Merriam-Webster]]|page=149|url=https://books.google.com/books?id=7C6V9zRxSPkC&lpg=PA149&pg=PA149#v=onepage&&f=false|isbn=0-87779-622-X}} At [[Google Books]].</ref> Which one of each pair is the opening quote mark and which is the closing quote varies between languages.
Similarly, the corner-brackets ｢ ｣ are quotation marks used in East Asian languages (see [[Quotation mark#Chinese, Japanese and Korean quotation marks|Quotation mark § Chinese, Japanese and Korean quotation marks]]).
In English, typographers generally prefer to not set brackets in [[italics]], even when the enclosed text is italic.<ref>Robert Bringhurst, ''The Elements of Typographic Style'', §5.3.2.</ref> However, in other languages like German, if brackets enclose text in italics, they are usually set in italics too.<ref>{{cite book |last1=Forsmann |first1=Friedrich |last2=DeJong |first2=Ralf |date=2004 |title=Detailtypografie |trans-title=Detail Typography |language=German |___location=Mainz |publisher= Herrmann Schmidt |page=263 |isbn= 978-3874396424}}</ref>
== Types and uses ==
=== Parentheses {{Anchor|Parenthesis}} ===
<!-- <onlyinclude> </onlyinclude> --> <!-- only include tag to avoid transclusion of the article bracket when someone writes this {{:)}}or {{:(}} -->
{{dablink|Various terms redirect here; for other uses, see [[Parenthesis (disambiguation)]], [[Paren (disambiguation)]], [[( ) (disambiguation)]], [[Parenthetical referencing]], and [[Parenthetical Girls]]}}
{{dablink|Due to [[Wikipedia:Naming conventions (technical restrictions)|technical restrictions]], titles like "<tt>:)</tt>" redirect here. For typographical portrayals of faces, see [[Emoticon]].}}
{{Wiktionary|parenthesis|( )}}
====Usage in writing====
Parentheses {{IPAc-en|p|ə|ˈ|r|ɛ|n|θ|ᵻ|s|iː|z}} (singular, parenthesis {{IPAc-en|p|ə|ˈ|r|ɛ|n|θ|ᵻ|s|ᵻ|s}}) (also called simply brackets, or round brackets, curved brackets, oval brackets, stalls or, colloquially, parens {{IPAc-en|p|ə|ˈ|r|ɛ|n|z}}) contain material that serves to clarify (in the manner of a [[gloss (annotation)|gloss]]) or is aside from the main point.<ref>{{cite web|last=Straus|first=Jane|author-link=Jane Straus|title=Parentheses — Punctuation Rules|url=http://www.grammarbook.com/punctuation/parens.asp|work=The Blue Book of Grammar and Punctuation|publisher=grammarbook.com|accessdate=18 April 2014}}</ref> A milder effect may be obtained by using a pair of commas as the [[delimiter]], though if the sentence contains commas for other purposes, visual confusion may result.
In American usage, parentheses are usually considered separate from other brackets, and calling them "brackets" is unusual.
Parentheses may be used in formal writing to add supplementary information, such as "Sen. John McCain (R-Arizona) spoke at length". They can also indicate shorthand for "[[uncertain plural|either singular or plural]]" for nouns, e. g. "the claim(s)". It can also be used for [[gender neutral language]], especially in languages with [[grammatical gender]], e. g. "(s)he agreed with his (her) physician".<ref>[[Slash (punctuation)#Gender-neutrality in Spanish and Portuguese]]</ref>
Parenthetical phrases have been used extensively in informal writing and stream of consciousness literature. Examples include the southern American author [[William Faulkner]] (see ''[[Absalom, Absalom!]]'' and [[The Sound and the Fury#Part 2: June 2, 1910|the Quentin section of ''The Sound and the Fury'']]) as well as poet [[E. E. Cummings]].
Parentheses have historically been used where the [[Em dash|dash]] is currently used in alternatives, such as "parenthesis)(parentheses". Examples of this usage can be seen in editions of ''[[A Dictionary of Modern English Usage|Fowler's]]''.
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]).<ref>{{cite web|last=Fogarty|first=Mignon|title=Parentheses, Brackets, and Braces|url=http://grammar.quickanddirtytips.com/parentheses-brackets-and-braces.aspx|publisher=Quick and Dirty Tips|accessdate=27 March 2011}}</ref>
Any punctuation inside parentheses or other brackets is independent of 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 (rhetoric)|parenthesis]]. (Parenthesized text is usually short and within a single sentence. Where several sentences of supplemental material are used in parentheses the final [[full stop]] would be within the parentheses, or simply omitted. Again, the parenthesis implies that the meaning and flow of the text is supplemental to the rest of the text and the whole would be unchanged were the parenthesized sentences removed.)
In more formal usage, "[[Parenthesis (rhetoric)|parenthesis]]" may refer to the entire bracketed text, not just to the punctuation marks used (so all the text in this set of round brackets may be said to be "a [[parenthesis (rhetoric)|parenthesis]]", "a parenthetical", or "a parenthetical phrase").<ref>{{cite web|url=http://www.thefreedictionary.com/parenthetical |title=The Free Online Dictionary |publisher=Thefreedictionary.com |date= |accessdate=2013-02-13}}</ref>
====Usage in enumerations====
;Unpaired parenthesis
Lower-case [[Latin letters]] used as indexes, rather than [[bullet (typography)|bullet]]s or numbers, followed by an unpaired parenthesis, are used in ordered [[wiktionary:list|list]]s especially in:
#[[education]]al testing,
#technical writing and diagrams,
#[[market research]], and
#[[elections]].{{citation needed|date=February 2018}}
====Usage as antisemitic symbol====
Since 2014, [[antisemite]]s have used [[triple parentheses]] around the names of people to denote them as Jewish.<ref name=mic>{{cite news|last1=Fleishman|first1=Cooper|last2=Smith|first2=Anthony|title=(((Echoes))), Exposed: The Secret Symbol Neo-Nazis Use to Target Jews Online|url=https://mic.com/articles/144228/echoes-exposed-the-secret-symbol-neo-nazis-use-to-target-jews-online#.sS1GX29cQ|accessdate=4 June 2016|publisher=Mic|date=1 June 2016}}</ref>
====Usage 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, {{math|2 + 3 × 4}} equals 14, since the multiplication is done before the addition. However, {{math|(2 + 3) × 4}} 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:
:<math>[(2 + 3) \times 4]^2 = 400.</math>
A related convention is that when parentheses have two levels of nesting, curly brackets (braces) are the outermost pair. Following this convention, when more than three levels of nesting are needed, often a cycle of parentheses, square brackets, and curly brackets will continue. This helps to distinguish between one such level and the next.<ref>{{cite web|url=http://math.about.com/od/mathhelpandtutorials/fl/Parenthesis-Braces-and-Brackets.html |title=Archived copy |accessdate=2014-08-01 |deadurl=yes |archiveurl=https://archive.is/20140806203819/http://math.about.com/od/mathhelpandtutorials/fl/Parenthesis-Braces-and-Brackets.html |archivedate=6 August 2014 }}</ref>
Parentheses are also used to set apart the [[Parameter|argument]]s in mathematical [[Function (mathematics)|function]]s. For example, {{math|''f''(''x'')}} is the function ''{{math|f}}'' applied to the [[Variable (mathematics)|variable]] ''{{math|x}}''. In [[coordinate system]]s parentheses are used to denote a set of coordinates; so in the [[Cartesian coordinate system]] {{math|(4, 7)}} may represent the point located at 4 on the ''x''-axis and 7 on the ''y''-axis.
Parentheses may also be used to represent a [[binomial coefficient]].
====Usage 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.
====Usage in other scientific fields====
Parentheses are used in [[chemistry]] to denote a [[polyatomic ion]].{{citation needed|date=February 2018}}
=== Square brackets {{Anchor|square bracket}} ===
{{Wiktionary|square bracket}}
====Usage
Square brackets—also called crotchets or simply brackets (US)—are mainly 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.<ref>''The Chicago Manual of Style, 15th ed.'', The University of Chicago Press, 2003, §6.104</ref>
A bracketed [[ellipsis]], […], is often used to indicate omitted material: "I'd like to thank [several unimportant people] for their tolerance [...]"<ref>{{cite web|url=http://www.bartleby.com/68/60/960.html |title=Bartleby.com: Great Books Online -- Quotes, Poems, Novels, Classics and hundreds more |work=bartleby.com |deadurl=yes |archiveurl=https://web.archive.org/web/20080524214802/http://www.bartleby.com/68/60/960.html |archivedate=24 May 2008 |df=dmy }}</ref>
Bracketed comments inserted into a quote indicate when 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 text is 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", it can be quoted succinctly as: "[P]olicymakers […] made use of economic analysis […] the way a drunkard uses a lamppost: for support, not illumination." When nested parentheses are needed, brackets are used as a substitute for the inner pair of parentheses within the outer pair.<ref>''The Chicago Manual of Style, 15th ed.'', The University of Chicago Press, 2003, §6.102 and §6.106</ref> 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".
The bracketed expression "[[sic|[''sic'']]]" is used after a quote or reprinted text to indicate the passage appears exactly as in the original source, where it may otherwise appear that a mistake has been made in reproduction.
In translated works, brackets are used to signify the same word or phrase in the original language to avoid ambiguity.<ref>''The Chicago Manual of Style, 15th ed.'', The University of Chicago Press, 2003, §6.105</ref>
For example: ''He is trained in the way of the open hand [karate].''
====Usage in proofreading====
Brackets (called ''move-left symbols'' or ''move right symbols'') are added to the sides of text in [[proofreading]] to indicate changes in indentation:
<center>
{| class="wikitable"
|-
! style="width:15%; text-align:left;"| Move left
| style="width:85%; text-align:left;"| [To Fate I sue, of other means bereft, the only refuge for the wretched left.
|-
! style="width:15%; text-align:left;"| Center
| style="width:85%; text-align:left;"| ]Paradise Lost[
|-
! style="width:15%; text-align:left;"| Move up
| style="width:85%; text-align:left;"| [[File:Quote to be Moved Up.svg|330px]]
|}
</center>
====Usage in scientific fields====
Brackets are used in [[mathematics]] in a variety of notations, including standard notations for [[interval (mathematics)|interval]]s, [[commutator]]s, the [[Floor and ceiling functions|floor function]], the [[Lie bracket of vector fields|Lie bracket]], [[Equivalence class#Notation and formal definition|equivalence classes]], the [[Iverson bracket]], and [[Matrix (mathematics)|matrices]]. Square brackets may also represent [[interval (mathematics)|interval]]s; ]0, 5[ for example, is the interval between 0 and 5, not including 0 or 5 (sometimes written (0,5)).
Brackets can also be used in [[chemistry]] to represent the [[concentration]] of a [[chemical substance]] or to denote distributed charge in a [[Complex (chemistry)|complex ion]].
Brackets are used in many computer [[programming language]]s, primarily to force the order of evaluation and for parameter lists and [[array data structure|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.
====Other uses====
In linguistics, [[phonetic transcription]]s are generally enclosed within brackets,<ref>''The Chicago Manual of Style, 15th ed.'', The University of Chicago Press, 2003, §6.107</ref> often using the [[International Phonetic Alphabet]], whereas [[phoneme|phonemic]] transcriptions typically use paired [[Slash (punctuation)|slash]]es. Pipes (| |) are often used to indicate a [[Morphophoneme|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.
Brackets are used to denote parts of the text that need to be checked when preparing drafts prior to finalizing a document. 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.
=== Curly brackets {{anchor|Braces|Curly bracket}} ===
{{Wiktionary|curly bracket}}
Curly brackets { and } are also called '''braces''' in the United States (or, colloquially, '''squiggly brackets'''). They are rarely used in prose and have no widely accepted use in formal writing, but may be used to mark words or that should be taken as a group, to avoid confusion when other types of brackets are already in use, or for a special purpose specific to the publication (such as in a dictionary).<ref>[https://english.stackexchange.com/questions/127892/are-curly-braces-ever-used-in-normal-text-if-not-why-were-they-created Are curly braces ever used in normal text? If not, why were they created?]</ref> More commonly, they are used to indicate a group of lines that should be taken together, as in when referring to several lines of poetry that should be repeated.
In music, they are known as [[accolade (notation)|accolade]]s or "[[brace (music)|braces]]", and connect two or more lines ([[Staff (music)|stave]]s) of music that are played simultaneously.<ref>[https://web.archive.org/web/20081202121802/http://www.decodeunicode.org/u%2B007B Decodeunicode.org > U+007B LEFT CURLY BRACKET] Retrieved on 3 May 2009</ref>
In [[mathematics]] they delimit [[Set (mathematics)|set]]s, and in writing, they may be used similarly, "Select your animal {goat, sheep, cow, horse} and follow me". In many programming languages, they enclose groups of [[Statement (programming)|statement]]s. Such languages ([[C (programming language)|C]] being one of the best-known examples) are therefore called [[curly bracket language]]s.<ref>{{cite web|url=http://www.riedquat.de/prog/style |title=Brace and Indent Styles and Code Convention |work=riedquat.de |deadurl=yes |archiveurl=https://web.archive.org/web/20150924070732/http://www.riedquat.de/prog/style |archivedate=24 September 2015 |df= }}</ref> In [[classical mechanics]], curly brackets are often also used to denote the [[Poisson bracket]] between two quantities.
=== Angle brackets {{anchor|Chevrons}} ===
{{refimprove section|date=November 2012}}
{{redirect|Angle bracket|a device used for joining|Angle bracket (fastener)}}
{{Wiktionary|angle bracket|chevron}}
[[Wikt:chevron|Chevrons]] {{angbr| }}, similar to the commonly used [[less-than symbol|less-than]] (<) and [[greater-than symbol]] (>), are often used to enclose highlighted material.
In physical sciences, chevrons are used to denote an average over time or over another continuous parameter. For example,
:<math>\left\langle V(t)^2 \right\rangle = \lim_{T\to\infty} \frac{1}{T}\int_{-\frac{T}{2}}^{\frac{T}{2}} V(t)^2\,{\rm{d}}t. </math>
The [[inner product]] of two vectors is commonly written as {{math|{{angbr|''a'',''b''}}}}, but the notation {{math|(''a'',''b'')}} is also used.
In mathematical physics, especially [[quantum mechanics]], it is common to write the inner product between elements as {{math|{{bra-ket|''a''|''b''}}}}, as a short version of {{math|{{bra|''a''}}·{{ket|''b''}}}}, or {{math|{{bra|''a''}}''Ô''{{ket|''b''}}}}, where {{math|''Ô''}} is an [[Operator (physics)|operator]]. This is known as [[Dirac notation]] or [[bra–ket notation]].
In [[set theory]], chevrons or parentheses are used to denote [[ordered pair]]s and other [[tuple]]s, whereas curly brackets are used for unordered sets.
In [[linguistics]], chevrons indicate [[grapheme]]s (i.e., written letters) or [[orthography]], as in "The English word {{IPA|/kæt/}} is spelled {{angbr|cat}}."<ref>{{cite book|last1=Bauer|first1=Laurie|title=The Linguistics Student's Handbook|date=2007|publisher=Edinburgh University Press|___location=Edinburgh|page=99|chapter-url=https://books.google.com/books?id=WsrtrmHkLvoC&pg=PA99|chapter=Notational conventions. Brackets}}</ref><ref name="Sampson">{{cite book|last1=Sampson|first1=Geoffrey|editor1-last=Allan|editor1-first=Keith|title=The Routledge Handbook of Linguistics|date=2016|publisher=Routledge|page=60|chapter-url=https://books.google.com/books?id=3vssCgAAQBAJ&pg=PA60|chapter=Writing systems: methods for recording language}}</ref><ref name="Trask"/>
In [[epigraphy]], they may be used for mechanical transliterations of a text into the Latin script.<ref name="Sampson"/>
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.<ref name="Trask">{{cite book|last1=Trask|first1=Robert Lawrence|title=The Dictionary of Historical and Comparative Linguistics|date=2000|publisher=Edinburgh University Press|___location=Edinburgh|page=22|chapter-url=https://books.google.com/books?id=EHeGzQ8wuLQC&pg=PA22|chapter=Angle brackets}}</ref>
Chevrons are infrequently used to denote words that are thought instead of spoken, such as:
:{{angbr| What an unusual flower! }}
The mathematical or logical symbols for ''greater-than'' (>) and ''less-than'' (<) are [[inequality (mathematics)|inequality]] symbols; when either symbol is bisected by a vertical line, it represents "not greater than" or "not less than," respectively. These [[symbol]]s are not punctuation marks when used, as intended, to represent an inequality. However, as true chevrons are not present on [[keyboard (computing)|computer keyboards]], the available less-than and greater-than symbols are often used instead. They are loosely referred to as ''angle[d] brackets'' or ''chevrons'' in this case, but more properly — and less confusingly — as ''pointy brackets'' (see the [[#Names for various bracket symbols|Names]] section above).{{citation needed|date=November 2012}}
Single and double pairs of comparison operators (<<, >>) (meaning ''much smaller than'' and ''much greater than'') are sometimes used as a fallback instead of [[guillemet]]s («, ») (used as [[non-English usage of quotation marks|quotation marks in many languages]]) when the proper characters are not available on the [[computer keyboard|keyboard]] nor in the [[input method editor|input editor]].
In [[comic book]]s, 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. Of course, since no foreign language is actually written, this is only ''notionally'' translated.{{Citation needed|date=March 2017}}
Chevron-like symbols are part of standard [[Chinese language|Chinese]], and [[Korean language|Korean]] punctuation, where they generally enclose the titles of books: ︿ and ﹀ or ︽ and ︾ for traditional [[tategaki|vertical printing]], and 〈 and 〉 or 《 and 》 for [[yokogaki|horizontal]] printing. See also [[non-English usage of quotation marks]].
In [[continuum mechanics]], chevrons may be used as [[Macaulay brackets]].
In [[non-English usage of quotation marks#Chinese, Japanese and Korean quotation marks|East Asian punctuation]], angle brackets are used as quotation marks.
=== Lenticular brackets ===
{{Wiktionary|【 】}}
Some [[East Asia|East Asian]] languages use lenticular brackets 【 】, a combination of square brackets and parentheses called {{lang|zh|方頭括號}} ''fāngtóu kuòhào'' in [[Chinese language|Chinese]] and {{lang|ja|
すみ付き}} ''sumitsuki'' in [[Japanese language|Japanese]]. They are used for inference{{clarification needed|date=April 2017}} in Chinese and used in titles and headings in Japanese.
=== Floor and ceiling corners ===
{{Wiktionary|⌊ ⌋|⌈ ⌉}}
The floor corner brackets ⌊ and ⌋, the ceiling corner brackets ⌈ and ⌉ are used to denote the integer [[floor and ceiling functions]].
=== Quine corners and half brackets ===
The Quine corners ⌜ and ⌝ have at least two uses in [[mathematical logic]]: either as [[quasi-quotation]], a generalization of quotation marks, or to denote the [[Gödel numbering|Gödel number]] of the enclosed [[Expression (mathematics)|expression]].
Half brackets are used in English to mark added text, such as in translations: "Bill saw ⸤her⸥".
In editions of [[papyrology|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.<ref>M.L. West (1973) ''Textual Criticism and Editorial Technique'' (Stuttgart) 81.</ref> 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.<ref name="Unicode Miscellaneous Technical"/>
=== Double brackets ===
Double brackets (or white square brackets), ⟦ ⟧, are used to indicate the ''semantic evaluation function'' in [[formal semantics (linguistics)|formal semantics]] for natural language and [[denotational semantics]] for programming languages.<ref>Dowty, D., Wall, R. and Peters, S.: 1981, Introduction to Montague semantics, Springer.</ref><ref>Scott, D. and Strachey, C.: 1971, Toward a mathematical semantics for computer languages, Oxford
University Computing Laboratory, Programming Research Group.</ref> The brackets stand for a function that maps a linguistic expression to its “denotation” or semantic value. Double brackets may also refer to the mathematical [[Floor_and_ceiling_functions|floor function]].
=== Brackets with quills ===
Known as "spike parentheses" ({{lang-sv|piggparenteser}}) ⁅ and ⁆ are used in Swedish dictionaries.<ref>See [[:sv:Parentes]]</ref>
==Specific uses==
===Computing===
The various bracket characters are frequently used in many [[Programming language|programming languages]] as [[operator (computer programming)|operator]]s or for other [[syntax (programming languages)|syntax]] markup. For instance, in [[C (programming language)|C]]-like languages, <code>{</code> and <code>}</code> are often used to delimit a [[code block]], and the parameters of [[method call]]s are generally enclosed by <code>(</code> and <code>)</code>.
In C, [[C++]], [[Java (programming language)|Java]] and other C-derived languages—as well as in [[Scheme (programming language)|Scheme]]-influenced languages that have adopted C/Java syntax, such as [[JavaScript]]—the "<code>{}</code>" symbols are referred to as "braces" or "curly braces" and never as brackets. Since the term "brace" is documented in the definitive programming specifications for these languages, it is preferable to use the correct term brace so there is no confusion between the brace (used to denote compound statements) and the bracket, used to denote other concepts, such as [[array data structure|array]] indices.<ref>Brian W. Kernighan, Dennis M. Ritchie. "The C Programming Language", 1988. p. 7. {{ISBN|0-13-110370-9}}</ref><ref>Bjarne Stroustrup, "The C++ Programming Language", 2013. p.39. {{ISBN|0-13-352285-7}}</ref>
===Mathematics===
{{main|Bracket (mathematics)}}
In addition to the use of [[#Parentheses ( )|parentheses]] to specify the [[order of operations]], both parentheses and brackets are used to denote an [[interval (mathematics)|interval]], also referred to as a half-open range. The notation {{closed-open|{{mvar|a}},{{mvar|c}}}} is used to indicate an interval from {{mvar|a}} to {{mvar|c}} that is inclusive of {{mvar|a}} but exclusive of {{mvar|c}}. That is, {{closed-open|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 set|finite]] number of 9s), but 12.0 is not included. In some European countries, the notation {{math|[5, 12[}} is also used for this. The endpoint adjoining the bracket is known as ''closed'', whereas 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 [[Extended real number line|+∞]] or −∞ is used as an endpoint, it is normally considered ''open'' and adjoined to a parenthesis. See [[Interval (mathematics)]] for a more complete treatment.
In [[quantum mechanics]], chevrons are also used as part of [[Paul Dirac|Dirac's]] formalism, [[bra–ket notation]], to note vectors from the [[dual space]]s of the Bra {{angbr|{{math|''A''|}} and the Ket {{math||''B''}}}}. Mathematicians will also commonly write {{angbr|{{math|''a'', ''b''}}}} for the [[inner product]] of two vectors. In statistical mechanics, chevrons denote ensemble or time average. Chevrons are used in [[group theory]] to write [[group presentation]]s, and to denote the [[group generators|subgroup generated]] by a collection of elements. Note that [[obtuse angle]]d chevrons are not always (and even not by all users) distinguished from a pair of less-than and greater-than signs <>, which are sometimes used as a [[typographic approximation]] of chevrons.
In [[group theory]] and [[ring theory]], brackets denote the [[commutator]]. In group theory, the commutator {{math|[{{mvar|g}}, {{mvar|h}}]}} is commonly defined as {{math|{{mvar|g}}<sup> −1</sup> {{mvar|h}}<sup> −1</sup> {{mvar|g}} {{mvar|h}} }}. In ring theory, the commutator {{math|[{{mvar|a}}, {{mvar|b}}]}} is defined as {{math|{{mvar|a}} {{mvar|b}} − {{mvar|b}} {{mvar|a}} }}. Furthermore, in ring theory, braces denote the [[anticommutator]] where {{math|{{{mvar|a}}, {{mvar|b}}}}} is defined as {{math|{{mvar|a}} {{mvar|b}} + {{mvar|b}} {{mvar|a}} }}. The bracket is also used to denote the [[Lie derivative]], or more generally the Lie bracket in any [[Lie algebra]].
Various notations, like the [[vinculum (symbol)|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 notation|Z]] [[formal specification]] language, braces define a set and chevrons define a sequence.
==
Traditionally in [[Accountancy|accounting]], contra amounts are placed in parentheses. A debit balance account in a series of credit balances will have brackets and vice versa.
===Law===
Brackets are used in some countries in the citation of [[law report]]s to identify parallel citations to non-official reporters. For example: Chronicle Pub. Co. v. [[Superior Court]], (1998) 54 Cal.2d 548, [7 Cal.Rptr. 109]. In some other countries (such as [[England 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, is in the 1954 volume of the Appeal Cases reports although the decision may have been given in 1953 or earlier, whereas (1954) 98 Sol Jo 176 reports a decision from 1954, in volume 98 of the Solicitor's Journal which may be published in 1955 or later.
When quoted material is in any way altered, the alterations are enclosed in brackets within the quotation. For example: Plaintiff asserts his cause is just, stating, "[m]y causes is [[sic|{{bracket|''sic''}}]] just." Although in the original quoted sentence the word "my" was capitalized, it has been modified in the quotation 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 "[''sic'']" (Latin for 'thus'). (''California Style Manual'', section 4:59 (4th ed.))
===Sports===
[[Bracket (tournament)|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 brackets or braces.
== {{anchor|Encoding}}Encoding in digital media ==
Representations of various kinds of brackets in [[Unicode]] and [[HTML]] are given below.
{|class="wikitable"
|-
!scope="col"| Usage !!colspan="2" scope="col"| Unicode !!scope="col"| SGML/[[List of HTML and XML character entities|HTML/XML entities]] !!scope="col"| Sample
|-
|rowspan="4"| General purpose<ref name="Basic Latin">{{citation | url=http://www.unicode.org/charts/PDF/U0000.pdf | title=C0 Controls and Basic Latin Code Chart | work=The Unicode Standard | accessdate=2016-02-27}}</ref>
| U+0028 || Left parenthesis || &#40; &lparen; ||rowspan="2"| (parentheses)
|-
| U+0029 || Right parenthesis || &#41; &rparen;
|-
| U+005B || Left square bracket || &#91; ||rowspan="2"| [''[[sic]]'']
|-
| U+005D || Right square bracket || &#93;
|-
|rowspan="4"| Technical/mathematical<br>(common)<ref name="Basic Latin"/>
| U+003C || Less-than sign || &#60; &lt; ||rowspan="2"| <HTML>
|-
| U+003E || Greater-than sign || &#62; &gt;
|-
| U+007B || Left curly bracket || &#123; ||rowspan="2"| {round, square, curly}
|-
|-
<!-- not brackets, see ==List of types==-->
|rowspan="10"| Quotation<br>(Western texts)<ref name="Latin-1 Supplement">{{citation | url=http://www.unicode.org/charts/PDF/U0080.pdf | title=C1 Controls and Latin-1 Supplement Code Chart | work=The Unicode Standard | accessdate=2016-02-27}}</ref><ref name="General Punctuation"/>
| U+00AB || Left-pointing double angle quotation mark || &#171; ||rowspan="2"| « French quote »
|-
| U+00BB || Right-pointing double angle quotation mark || &#187;
|-
| U+2039|| Single left-pointing angle quotation mark || &#8249; ||rowspan="2"| ‹ ''{{math|x}}'' ›
|-
| U+203A || Single right-pointing angle quotation mark || &#8250;
|-
| U+201C || Left double quotation mark || &#8220; ||rowspan="2"| “English quote”
|-
| U+201D || Right double quotation mark || &#8221;
|-
| U+2018 || Left single quotation mark || &#8216; ||rowspan="2"| ‘English quote’
|-
| U+2019 || Right single quotation mark || &#8217;
|-
| U+201A || Single low-9 quotation mark || &#8218; &sbquo; || ‚German quote‘ or ‚Polish quote’
|-
| U+201E || Double low-9 quotation mark || &#8222; &bdquo; || „German quote“ or „Polish quote”
|-
|rowspan="4"| [[Floor and ceiling functions]]<ref name="Unicode Miscellaneous Technical">{{citation | url=http://www.unicode.org/charts/PDF/U2300.pdf | title=Miscellaneous Technical Code Chart | work=The Unicode Standard | accessdate=2016-02-27}}</ref>
| U+2308 || Left ceiling || &#8968; ||rowspan="2"| ⌈''ceiling''⌉
|-
| U+2309 || Right ceiling || &#8969;
|-
| U+230A || Left floor || &#8970; ||rowspan="2"| ⌊''floor''⌋
|-
| U+230B || Right floor || &#8971;
|-
|rowspan="4"| [[quasi-quotation|Quine corners]]<ref name="Unicode Miscellaneous Technical"/>
| U+231C || Top left corner || &#8988; ||rowspan="2"| ⌜''quasi-quotation''⌝<br>⌜''editorial notation''⌝
|-
| U+231D || Top right corner || &#8989;
|-
| U+231E || Bottom left corner || &#8990; ||rowspan="2"| ⌞''editorial notation''⌟
|-
| U+231F || Bottom right corner || &#8991;
|-
|rowspan="79"| Technical/mathematical<br>(specialized)<ref name="Unicode Miscellaneous Technical" /><ref>{{citation | url=http://www.unicode.org/charts/PDF/U2070.pdf|title=Superscripts and Subscripts Code Chart|work=The Unicode Standard|accessdate=2016-02-27}}</ref><ref name="Unicode Miscellaneous Mathematical Symbols-A">{{citation | url=http://www.unicode.org/charts/PDF/U27C0.pdf | title=Miscellaneous Mathematical Symbols-A Code Chart | work=The Unicode Standard | accessdate=2016-02-27}}</ref><ref name="Unicode Miscellaneous Mathematical Symbols-B">{{citation | url=http://www.unicode.org/charts/PDF/U2980.pdf | title=Miscellaneous Mathematical Symbols-B Code Chart | work=The Unicode Standard | accessdate=2016-02-27}}</ref>
|-
| U+207D || Superscript left parenthesis || &#8317; ||rowspan="2"| X⁽²⁾
|-
| U+207E || Superscript right parenthesis || &#8318;
|-
| U+208D || Subscript left parenthesis || &#8333; ||rowspan="2" | X₍₂₎
|-
| U+208E || Subscript right parenthesis || &#8334;
|-
| U+239B || Left parenthesis upper hook || &#9115; ||rowspan="6"|
{|
| ⎛<br/>⎜<br/>⎝
| large parentheses
|⎞<br/>⎟<br/>⎠
|}
|-
| U+239C || Left parenthesis extension || &#9116;
|-
| U+239D || Left parenthesis lower hook || &#9117;
|-
| U+239E || Right parenthesis upper hook || &#9118;
|-
| U+239F || Right parenthesis extension || &#9119;
|-
| U+23A0 || Right parenthesis lower hook || &#9120;
|-
| U+23A1 || Left square bracket upper corner || &#9121; ||rowspan="6"|
{|
| ⎡<br/>⎢<br/>⎣
| large square brackets
| ⎤<br/>⎥<br/>⎦
|}
|-
| U+23A2 || Left square bracket extension || &#9122;
|-
| U+23A3 || Left square bracket lower corner || &#9123;
|-
| U+23A4 || Right square bracket upper corner || &#9124;
|-
| U+23A5 || Right square bracket extension || &#9125;
|-
| U+23A6 || Right square bracket lower corner || &#9126;
|-
| U+23A7 || Left curly bracket upper hook || &#9127; ||rowspan="6"|
{|
| ⎧<br/>⎨<br/>⎩
| large curly brackets
| ⎫<br/>⎬<br/>⎭
|}
|-
| U+23A8 || Left curly bracket middle piece || &#9128;
|-
| U+23A9 || Left curly bracket lower hook || &#9129;
|-
| U+23AB || Right curly bracket upper hook || &#9131;
|-
| U+23AC || Right curly bracket middle piece || &#9132;
|-
| U+23AD || Right curly bracket lower hook || &#9133;
|-
| U+23AA || Curly bracket extension || &#9130; || ⎪
|-
| U+23B0 || Upper left or lower right curly bracket section || &#9136; ||rowspan="2"| ⎰ ⎱<br>⎱ ⎰
|-
| U+23B1 || Upper right or lower left curly bracket section || &#9137;
|-
| U+23B4 || Top square bracket || &#9140; ||rowspan="2"|
{| style="text-align: center;"
|-
| ⎴
|-
| horizontal square brackets
|-
| ⎵
|}
|-
| U+23B5 || Bottom square bracket || &#9141;
|-
| U+23B6 || Bottom square bracket over top square bracket || &#9142; ||
{|style="text-align: center; font-style:monospace"
|-
| ⎴ || ⎴ || ⎴ || ⎴ || ⎴ || ⎴ || ⎴ || ⎴ || ⎴
|-
| t || e || r || m || i || n || a || l ||
|-
| ⎶ || ⎶ || ⎶ || ⎶ || ⎶ || ⎶ || ⎶ || ⎶ || ⎶
|-
| e || m || u || l || a || t || i || o || n
|-
| ⎵ || ⎵ || ⎵ || ⎵ || ⎵ || ⎵ || ⎵ || ⎵ || ⎵
|}
|-
| U+23B8 || Left vertical box line || &#9144; ||rowspan="2"|⎸boxed text⎹
|-
| U+23B9 || Right vertical box line || &#9145;
|-
| U+23DC || Top parenthesis || &#9180; ||rowspan="2"|
{| style="text-align: center;"
|-
| ⏜
|-
| horizontal parentheses
|-
| ⏝
|}
|-
| U+23DD || Bottom parenthesis || &#9181;
|-
| U+23DE || Top curly bracket || &#9182; ||rowspan="2"|
{| style="text-align: center;"
|-
| ⏞
|-
| horizontal curly brackets
|-
| ⏟
|}
|-
| U+23DF || Bottom curly bracket || &#9183;
|-
| U+23E0 || Top tortoise shell bracket || &#9184; ||rowspan="2"|
{| style="text-align: center;"
|-
| ⏠
|-
| tortoise shell brackets
|-
| ⏡
|}
|-
| U+23E1 || Bottom tortoise shell bracket || &#9185;
|-
| U+27C5 || Left s-shaped bag delimiter || &#10181; ||rowspan="2"| ⟅…⟆
|-
| U+27C6 || Right s-shaped bag delimiter || &#10182;
|-
| U+27D3 || Lower right corner with dot || &#10195; ||rowspan="2"| ⟓pullback…pushout⟔
|-
| U+27D4 || Upper left corner with dot || &#10196;
|-
| U+27E6 || Mathematical left white square bracket || &#10214; ||rowspan="2"| ⟦white square brackets⟧
|-
| U+27E7 || Mathematical right white square bracket || &#10215;
|-
| U+27E8 || Mathematical left angle bracket || &#10216; &lang;<ref name="lang-rang" group="e"/> ||rowspan="2"| {{angbr|''{{math|a}}'', ''{{math|b}}''}}
|-
| U+27E9 || Mathematical right angle bracket || &#10217; &rang;<ref name="lang-rang" group="e"/>
|-
| U+27EA || Mathematical left double angle bracket || &#10218; ||rowspan="2"| ⟪''{{math|A}}'', ''{{math|B}}''⟫
|-
| U+27EB || Mathematical right double angle bracket || &#10219;
|-
| U+27EC || Mathematical left white tortoise shell bracket || &#10220; ||rowspan="2"| ⟬white tortoise shell brackets⟭
|-
| U+27ED || Mathematical right white tortoise shell bracket || &#10221;
|-
| U+27EE || Mathematical left flattened parenthesis || &#10222; ||rowspan="2"| ⟮flattened parentheses⟯
|-
| U+27EF || Mathematical right flattened parenthesis || &#10223;
|-
| U+2983 || Left white curly bracket || &#10627; ||rowspan="2"| ⦃white curly brackets⦄
|-
| U+2984 || Right white curly bracket || &#10628;
|-
| U+2985 || Left white parenthesis || &#10629; ||rowspan="2"| ⦅white/double parentheses⦆
|-
| U+2986 || Right white parenthesis || &#10630;
|-
| U+2987 || [[Z notation]] left image bracket || &#10631; ||rowspan="2"| ''{{math|R}}''⦇''{{math|S}}''⦈
|-
| U+2988 || Z notation right image bracket || &#10632;
|-
| U+2989 || Z notation left binding bracket || &#10633; ||rowspan="2"| ''{{math|A}}''⦉''{{math|B}}''⦊
|-
| U+298A || Z notation right binding bracket || &#10634;
|-
| U+298B || Left square bracket with underbar || &#10635; ||rowspan="2"| ⦋underlined square brackets⦌
|-
| U+298C || Right square bracket with underbar || &#10636;
|-
| U+298D || Left square bracket with tick in top corner || &#10637; ||rowspan="2"| ⦍ticked square brackets⦐
|-
| U+2990 || Right square bracket with tick in top corner || &#10640;
|-
| U+298E || Right square bracket with tick in bottom corner || &#10638; ||rowspan="2"| ⦏ticked square brackets⦎
|-
| U+298F || Left square bracket with tick in bottom corner || &#10639;
|-
| U+2991 || Left angle bracket with dot || &#10641; ||rowspan="2"| ⦑dotted angle brackets⦒
|-
| U+2992 || Right angle bracket with dot || &#10642;
|-
| U+2993 || Left arc less-than bracket || &#10643; ||rowspan="2"| ⦓[[Inequality (mathematics)|inequality]] sign brackets⦔
|-
| U+2994 || Right arc greater-than bracket || &#10644;
|-
| U+2995 || Double left arc greater-than bracket || &#10645; ||rowspan="2"| ⦕inequality sign brackets⦖
|-
| U+2996 || Double right arc less-than bracket || &#10646;
|-
| U+2997 || Left black tortoise shell bracket || &#10647; ||rowspan="2"| ⦗black tortoise shell brackets⦘
|-
| U+2998 || Right black tortoise shell bracket || &#10648;
|-
| U+29D8 || Left wiggly fence || &#10712; ||rowspan="2"| ⧘…⧙
|-
| U+29D9 || Right wiggly fence || &#10713;
|-
| U+29DA || Left double wiggly fence || &#10714; ||rowspan="2"| ⧚…⧛
|-
| U+29DB || Right double wiggly fence || &#10715;
|-
| U+29FC || Left-pointing curved angle bracket || &#10748; ||rowspan="2"| ⧼…⧽
|-
| U+29FD || Right-pointing curved angle bracket || &#10749;
|-
|rowspan="4"| Half brackets<ref name="Supplemental Punctuation">{{citation | url=http://www.unicode.org/charts/PDF/U2E00.pdf | title=Supplemental Punctuation Code Chart | work=The Unicode Standard | accessdate=2016-02-27}}</ref>
| U+2E22 || Top left half bracket || &#11810; ||rowspan="2"| ⸢''editorial notation''⸣
|-
| U+2E23 || Top right half bracket || &#11811;
|-
| U+2E24 || Bottom left half bracket || &#11812; ||rowspan="2"| ⸤''editorial notation''⸥
|-
| U+2E25 || Bottom right half bracket || &#11813;
|-
|rowspan="14"| [[Dingbat]]s<ref>{{citation | url=http://www.unicode.org/charts/PDF/U2700.pdf | title=Dingbats Code Chart | work=The Unicode Standard | accessdate=2016-02-27}}</ref>
| U+2768 || Medium left parenthesis ornament || &#10088; ||rowspan="2"| ❨medium parenthesis ornament❩
|-
| U+2769 || Medium right parenthesis ornament || &#10089;
|-
| U+276A || Medium flattened left parenthesis ornament || &#10090; ||rowspan="2"| ❪medium flattened parenthesis ornament❫
|-
| U+276B || Medium flattened right parenthesis ornament || &#10091;
|-
| U+276C || Medium left-pointing angle bracket ornament || &#10092; ||rowspan="2"| ❬medium angle bracket ornament❭
|-
| U+276D || Medium right-pointing angle bracket ornament || &#10093;
|-
| U+2770 || Heavy left-pointing angle bracket ornament || &#10096; ||rowspan="2"| ❰heavy angle bracket ornament❱
|-
| U+2771 || Heavy right-pointing angle bracket ornament || &#10097;
|-
| U+276E || Heavy left-pointing angle quotation mark ornament || &#10094; ||rowspan="2"| ❮heavy angle quotation ornament❯
|-
| U+276F || Heavy right-pointing angle quotation mark ornament || &#10095;
|-
| U+2772 || Light left tortoise shell bracket ornament || &#10098; ||rowspan="2"| ❲light tortoise shell bracket ornament❳
|-
| U+2773 || Light right tortoise shell bracket ornament || &#10099;
|-
| U+2774 || Medium left curly bracket ornament || &#10100; ||rowspan="2"| ❴medium curly bracket ornament❵
|-
| U+2775 || Medium right curly bracket ornament || &#10101;
|-
|rowspan="2"| [[Arabic script|Arabic]]<ref>{{citation | url=http://www.unicode.org/charts/PDF/UFB50.pdf | title=Arabic Presentation Forms-A Code Chart | work=The Unicode Standard | accessdate=2016-02-27}}</ref>
| U+FD3E || Ornate left parenthesis || &#64830; ||rowspan="2"| {{script/Arabic|﴿العربية﴾}}
|-
| U+FD3F || Ornate right parenthesis || &#64831;
|-
|rowspan="2"| [[N'Ko alphabet|N'Ko]]<ref name="Supplemental Punctuation"/>
| U+2E1C || Left low paraphrase bracket || &#11804; ||rowspan="2"| {{script|Nkoo|⸜ߒߞߏ⸝}}
|-
| U+2E1D || Right low paraphrase bracket || &#11805;
|-
|rowspan="2"| [[Ogham]]<ref>{{citation | url=http://www.unicode.org/charts/PDF/U1680.pdf | title=Ogham Code Chart | work=The Unicode Standard | accessdate=2016-02-27}}</ref>
| U+169B || Ogham feather mark || &#5787; ||rowspan="2"| <big>᚛ᚑᚌᚐᚋ᚜</big>
|-
| U+169C || Ogham reversed feather mark || &#5788;
|-
| [[Old Hungarian alphabet|Old Hungarian]] || U+2E42 || Double low-reversed-9 quotation mark || &#11842;
|-
|rowspan="4"| [[Tibetan alphabet|Tibetan]]<ref>{{citation | url=http://www.unicode.org/charts/PDF/U0F00.pdf | title=Tibetan Code Chart | work=The Unicode Standard | accessdate=2016-02-27}}</ref>
| U+0F3A || Tibetan mark gug rtags gyon || &#3898; ||rowspan="2"| <big>༺དབུ་ཅན་༻</big>
|-
| U+0F3B || Tibetan mark gug rtags gyas || &#3899;
|-
| U+0F3C || Tibetan mark ang khang gyon || &#3900; ||rowspan="2"| <big>༼༡༢༣༽</big>
|-
| U+0F3D || Tibetan mark ang khang gyas || &#3901;
|-
|rowspan="8"| [[New Testament]] editorial marks<ref name="Supplemental Punctuation"/>
| U+2E02 || Left substitution bracket || &#11778; ||rowspan="2"| ⸂…⸃
|-
| U+2E03 || Right substitution bracket || &#11779;
|-
| U+2E04 || Left dotted substitution bracket || &#11780; ||rowspan="2"| ⸄…⸅
|-
| U+2E05 || Right dotted substitution bracket || &#11781;
|-
| U+2E09 || Left transposition bracket || &#11785; ||rowspan="2"| ⸉…⸊
|-
| U+2E0A || Right transposition bracket || &#11786;
|-
| U+2E0C || Left raised omission bracket || &#11788; ||rowspan="2"| ⸌…⸍
|-
| U+2E0D || Right raised omission bracket || &#11789;
|-
|rowspan="6"| [[Medieval studies]]<ref name="General Punctuation">{{citation | url=http://www.unicode.org/charts/PDF/U2000.pdf | title=General Punctuation Code Chart | work=The Unicode Standard | accessdate=2016-03-01}}</ref><ref name="Supplemental Punctuation"/>
| U+2045 || Left square bracket with quill || &#8261; ||rowspan="2"|⁅…⁆
|-
| U+2046 || Right square bracket with quill || &#8262;
|-
| U+2E26 || Left sideways u bracket || &#11814; ||rowspan="2"| ⸦crux⸧
|-
| U+2E27 || Right sideways u bracket || &#11815;
|-
| U+2E28 || Left double parenthesis || &#11816; ||rowspan="2"| ⸨…⸩
|-
| U+2E29 || Right double parenthesis || &#11817;
|-
|rowspan="10"| Quotation<br>(East-Asian texts)<ref name="CJK Symbols and Punctuation"/>
| U+3014 || Left tortoise shell bracket || &#12308; ||rowspan="2"| 〔…〕
|-
| U+3015 || Right tortoise shell bracket || &#12309;
|-
| U+3016 || Left white lenticular bracket || &#12310; ||rowspan="2"| 〖…〗
|-
| U+3017 || Right white lenticular bracket || &#12311;
|-
| U+3018 || Left white tortoise shell bracket || &#12312; ||rowspan="2"| 〘…〙
|-
| U+3019 || Right white tortoise shell bracket || &#12313;
|-
| U+301A || Left white square bracket || &#12314; ||rowspan="2"| 〚…〛
|-
| U+301B || Right white square bracket || &#12315;
|-
| U+301D || Reversed double prime quotation mark || &#12317; ||rowspan="2"| 〝…〞
|-
| U+301E || Double prime quotation mark || &#12318;<ref name="301E" group="e"/>
|-
|rowspan="4"| Quotation<br>(halfwidth East-Asian texts)<ref name="Unicode Miscellaneous Technical"/><ref name="Halfwidth and Fullwidth Forms"/>
| U+2329 || Left-pointing angle bracket || &#9001; &lang;<ref name="lang-rang" group="e"/> || rowspan="2" | 〈deprecated〉
|-
| U+232A || Right-pointing angle bracket || &#9002; &rang;<ref name="lang-rang" group="e"/>
|-
| U+FF62 || Halfwidth left corner bracket || &#65378; ||rowspan="2"| ｢ｶﾀｶﾅ｣
|-
| U+FF63 || Halfwidth right corner bracket || &#65379;
|-
|rowspan="10"| Quotation<br>(fullwidth East-Asian texts)<ref name="CJK Symbols and Punctuation">{{citation | url=http://www.unicode.org/charts/PDF/U3000.pdf | title=CJK Symbols and Punctuation Code Chart | work=The Unicode Standard | accessdate=2016-02-27}}</ref>
| U+3008 || Left angle bracket || &#12296; ||rowspan="2"| 〈한〉
|-
| U+3009 || Right angle bracket || &#12297;
|-
| U+300A || Left double angle bracket || &#12298; ||rowspan="2"| 《한》
|-
| U+300B || Right double angle bracket || &#12299;
|-
| U+300C || Left corner bracket || &#12300; ||rowspan="2"| 「白八櫨」
|-
| U+300D || Right corner bracket || &#12301;
|-
| U+300E || Left white corner bracket || &#12302; ||rowspan="2"| 『カタカナ』
|-
| U+300F || Right white corner bracket || &#12303;
|-
| U+3010 || Left black lenticular bracket || &#12304; ||rowspan="2"| 【ひらがな】
|-
| U+3011 || Right black lenticular bracket || &#12305;
|-
|rowspan="4"| General purpose<br> (fullwidth East-Asian)<ref name="Halfwidth and Fullwidth Forms">{{citation | url=http://www.unicode.org/charts/PDF/UFF00.pdf | title=Halfwidth and Fullwidth Forms Code Chart | work=The Unicode Standard | accessdate=2016-02-27}}</ref>
| U+FF08 || Fullwidth left parenthesis || &#65288; ||rowspan="2"| （Ｗｉｋｉ）
|-
| U+FF09 || Fullwidth right parenthesis || &#65289;
|-
| U+FF3B || Fullwidth left square bracket || &#65339; ||rowspan="2"| ［''ｓｉｃ''］
|-
| U+FF3D || Fullwidth right square bracket || &#65341;
|-
|rowspan="6"| Technical/mathematical<br>(fullwidth East-Asian)<ref name="Halfwidth and Fullwidth Forms"/>
| U+FF1C || Fullwidth less-than sign || &#65308; ||rowspan="2"| ＜ＨＴＭＬ＞
|-
| U+FF1E || Fullwidth greater-than sign || &#65310;
|-
| U+FF5B || Fullwidth left curly bracket || &#65371; ||rowspan="2"| ｛１、２｝
|-
| U+FF5D || Fullwidth right curly bracket || &#65373;
|-
| U+FF5F || Fullwidth left white parenthesis || &#65375; ||rowspan="2"| ｟…｠
|-
| U+FF60 || Fullwidth right white parenthesis || &#65376;
|}
<references group="e">
<ref name="lang-rang">&lang; and &rang; 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 in [http://www.w3.org/TR/xml-entity-names/#diff-xhtml1 XML Entity Definitions for Characters].</ref>
<ref name="301E">This is fullwidth version of U+2033 DOUBLE PRIME. In vertical texts, U+301F LOW DOUBLE PRIME QUOTATION MARK is preferred.</ref>
</references>
Braces (curly brackets) first became part of a character set with the 8-bit code of the [[IBM 7030 Stretch]].<ref>{{cite web |last=Bob |first=Bemer |title=The Great Curly Brace Trace Chase |url=http://www.bobbemer.com/BRACES.HTM |accessdate =2009-09-05 |postscript=<!--None-->}}</ref>
The angle brackets or chevrons at U+27E8 and U+27E9 are for mathematical use and Western languages, whereas U+3008 and U+3009 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,<ref name="Unicode Miscellaneous Technical" /> because they are canonically equivalent to the CJK code points U+300x and thus likely to render as double-width symbols. The ''less-than'' and ''greater-than'' symbols are often used as replacements for chevrons.
==See also==
* [[International variation in quotation marks]]
* [[Emoticon]]
* [[Japanese typographic symbols]]
* [[Order of operations]]
==References==
{{Reflist|30em}}
==Bibliography==
* {{cite book |authorlink=John Lennard |last=Lennard |first=John |title=But I Digress: The Exploitation of Parentheses in English Printed Verse |year=1991 |isbn=0-19-811247-5 |publisher=Clarendon Press |___location=Oxford}}
* {{cite book |last=Turnbull |title=The Graphics of Communication |publisher=Holt |___location=New York |year=1964|display-authors=etal}} 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.
==External links==
*{{commons category-inline|Brackets (punctuation marks)|Brackets}}
*{{wiktionary-inline|bracket}}
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