View source for Bracket

{{Short description|Punctuation mark}}
{{About|the family of punctuation marks}}
{{More citations needed|date=March 2022}}
{{EngvarB|date=November 2020}}
{{Use dmy dates|date=May 2016}}
{{Infobox punctuation mark
 |name     = Brackets
 |variant1 = (&nbsp;)
 |caption1 = Brackets ([[British English|BE]])<br />{{nobold|or}}<br />parentheses ([[American English|AE]])<br />{{nobold|or}}<br />round brackets (BE){{sfn|Pointon|Clark|2014|p=406}}
 |variant2 = [&nbsp;]
 |caption2 = Square brackets (BE)<br />{{nobold|or}}<br />brackets (AE){{sfn|Pointon|Clark|2014|p=406}}
 |variant3 = {&nbsp;}
 |caption3 = Braces (BE&AE)<br />{{nobold|or}}<br />curly brackets (BE){{sfn|Pointon|Clark|2014|p=406}}
 |variant4 = ⟨&nbsp;⟩
 |caption4 = Angle brackets (BE&AE){{sfn|Pointon|Clark|2014|p=406}}<br />{{nobold|or}}<br />chevrons{{sp}}{{nobold|<ref>{{cite web | url=https://www.thesaurus.com/e/grammar/angle-brackets/ | title=What Are Angle Brackets ( < ) and How do You Use Them? | date=16 March 2022 }}</ref>}}
}}
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.{{sfn|McArthur|McArthur|2005}} 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 English|British]] and [[American English]].{{sfn|Pointon|Clark|2014|p=406}} "Brackets", without further qualification, are in British English the {{char|(}}...{{char|)}} marks and in American English the {{char|[}}...{{char|]}} marks.{{sfn|Pointon|Clark|2014|p=406}}{{sfn|McArthur|McArthur|2005}}

Other minor bracket shapes exist, such as (for example) ''slash'' or ''diagonal'' brackets used by linguists to enclose [[phonemes]].{{sfn|Peters|2007|p=101}}

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",<ref name="unicode-9">{{cite web |url= https://www.unicode.org/reports/tr9/#Paired_Brackets |title=Unicode Bidirectional Algorithm |at=§ 3.1.3 Paired Brackets |access-date=24 April 2018 |website=Unicode Technical Reports |publisher=Unicode Consortium |archive-date=3 October 2018 |archive-url= https://web.archive.org/web/20181003140816/http://www.unicode.org/reports/tr9/#Paired_Brackets |url-status=live}}</ref> respectively, depending on the [[Writing system#Directionality|directionality]] of the context.

In casual writing and in technical fields such as computing or linguistic analysis of [[grammar]], brackets [[nesting (computing)|nest]], with segments of bracketed material containing embedded within them other further bracketed sub-segments.{{sfn|McArthur|McArthur|2005}} The number of opening brackets matches the number of closing brackets in such cases.{{sfn|McArthur|McArthur|2005}}

[[Glossary of mathematical symbols#Brackets|Various forms of brackets are used in mathematics]], with specific mathematical meanings, often for denoting specific [[function (mathematics)|mathematical functions]] and [[subformula]]s.

==History==
Angle brackets or [[Wikt:chevron|chevrons]] '''⟨&nbsp;⟩''' were the earliest type of bracket to appear in [[written English]]. [[Desiderius Erasmus|Erasmus]] coined the term {{lang|la|lunula}} to refer to the round brackets or [[Wikt:parenthesis|parentheses]] '''({{nbsp}})''' recalling the shape of the [[Crescent|crescent moon]] ({{langx|la|luna}}).<ref>{{cite book |last=Truss |first=Lynne |author-link=Lynn Truss |title=[[Eats, Shoots & Leaves]] |date=2003 |page=161 |isbn=1592400876}}</ref>

Most typewriters only had the left and right parentheses. Square brackets appeared with some teleprinters.

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 |access-date=5 September 2009 |archive-url= https://web.archive.org/web/20090903184346/http://www.bobbemer.com/BRACES.HTM |archive-date=3 September 2009}}</ref>

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.<ref>{{cite book |first=Robert |last=Bringhurst |title=The Elements of Typographic Style |at=§5.3.2}}</ref> However, in other languages like German, if brackets enclose text in italics, they are usually also set in italics.<ref>{{cite book |last1=Forsmann |first1=Friedrich |last2=DeJong |first2=Ralf |date=2004 |title=Detailtypografie |trans-title=Detail Typography |language=de |location=Mainz |publisher=Herrmann Schmidt |page=263 |isbn=9783874396424}}</ref>

==Parentheses or round brackets<span class="anchor" id="Parenthesis"></span><span class="anchor" id="Parentheses"></span><span class="anchor" id="Round brackets"></span>==
{{redirect several|Parenthesis|Paren|Parens|( )}}
{{Technical reasons|:)|the keyboard symbols|List of emoticons|the generic smiling face|Smiley}}
{{original research|section|date=March 2022}}
{{Infobox punctuation mark
 |name     = Parenthesis
 |variant1 = (&nbsp;)
 |caption1 = {{ubl|parentheses ([[American English|AE]])|brackets ([[British English|BE]])|round brackets (BE){{sfn|Pointon|Clark|2014|p=406}}}}
 |unicode_list =
<div style="text-align:left;">
;General purpose {{nwr|(half-width):<ref name="Basic Latin"/>}}
:* {{unichar|0028|Left parenthesis|html=}}
:* {{unichar|0029|Right parenthesis|html=}}
;General purpose {{nwr|(full-width East Asian):<ref name="Halfwidth and Fullwidth Forms" />}}
:* {{unichar|FF08|Fullwidth left parenthesis|html=}}
:* {{unichar|FF09|Fullwidth right parenthesis|html=}}
{{collapsible list|bullets=yes|title=[[Arabic script]]{{br}}(Quranic quotations)<ref name="Unicode Arabic Presentation Forms"/>|
|{{unichar|FD3E|Ornate left parenthesis|html=}}
|{{unichar|FD3F|Ornate right parenthesis|html=}}
}}
{{collapsible list|bullets=yes|title=[[Mediaeval studies]]<ref name="General Punctuation"/><ref name="Supplemental Punctuation" />|
|{{unichar|2E28|Left double parenthesis|html=}}
|{{unichar|2E29|Right double parenthesis|html=}}
}}
{{collapsible list|bullets=yes|title=Technical<ref name="Unicode Miscellaneous Technical" /><ref name="Unicode Superscripts and Subscripts"/><ref name="Unicode Miscellaneous Mathematical Symbols-A"/><ref name="Unicode Miscellaneous Mathematical Symbols-B"/>|
|{{unichar|207D|Superscript left parenthesis|html=}}
|{{unichar|207E|Superscript right parenthesis|html=}}
|{{unichar|208D|Subscript left parenthesis|html=}}
|{{unichar|208E|Subscript right parenthesis|html=}}
|{{unichar|239B|Left parenthesis upper hook|html=}}
|{{unichar|239C|Left parenthesis extension|html=}}
|{{unichar|239D|Left parenthesis lower hook|html=}}
|{{unichar|239E|Right parenthesis upper hook|html=}}
|{{unichar|239F|Right parenthesis extension|html=}}
|{{unichar|23A0|Right parenthesis lower hook|html=}}
|{{unichar|23DC|Top parenthesis|html=}}
|{{unichar|23DD|Bottom parenthesis|html=}}
|{{unichar|27EE|Mathematical left flattened parenthesis|html=}}
|{{unichar|27EF|Mathematical right flattened parenthesis|html=}}
|{{unichar|2983|Left white curly bracket|html=}}
|{{unichar|2984|Right white curly bracket|html=}}
|{{unichar|2985|Left white parenthesis|html=}}
|{{unichar|2986|Right white parenthesis|html=}}
}}
{{collapsible list|bullets=yes|title=Phonetic punctuation<ref name="Unicode Phonetic Punctuation"/>|
|{{unichar|2E59|Top half left parenthesis|html=}}
|{{unichar|2E5A|Top half right parenthesis|html=}}
|{{unichar|2E5B|Bottom half left parenthesis|html=}}
|{{unichar|2E5C|Bottom half right parenthesis|html=}}
}}
{{collapsible list|bullets=yes|title=[[Dingbat]]s<ref name="Unicode Dingbats"/>|
|{{unichar|2768|Medium left parenthesis ornament|html=}}
|{{unichar|2769|Medium right parenthesis ornament|html=}}
|{{unichar|276A|Medium flattened left parenthesis ornament|html=}}
|{{unichar|276B|Medium flattened right parenthesis ornament|html=}}
}}
</div>
}}
{{Wiktionary|parenthesis|round bracket|(&nbsp;)|(|)}}
<!-- <onlyinclude> </onlyinclude> --> <!-- only include tag to avoid transclusion of the article bracket when someone writes this {{:)}}or {{:(}} -->

{{char|(}} and {{char|)}} are ''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}}) in American English, and either ''round brackets'' or simply ''brackets'' in British English.{{sfn|Pointon|Clark|2014|p=406}}{{sfn|Peters|2007|p=101}}
They are also known as "parens" {{IPAc-en|p|ə|ˈ|r|ɛ|n|z}}, "circle brackets", or "smooth brackets".

In formal writing, "parentheses" is also used in British English.{{Citation needed|date=November 2023}}

===Uses of ( )<span class="anchor" id="Uses of parentheses"></span><span class="anchor" id="Uses of round brackets"></span>===
Parentheses contain [[adjunctive]] material that serves to clarify (in the manner of a [[gloss (annotation)|gloss]]) or is aside from the main point.<ref>{{cite web |last1=Straus |first1=Jane |author1-link=Jane Straus |last2=Kaufman |first2=Lester |title=Parentheses—Punctuation Rules |url=https://www.grammarbook.com/punctuation/parens.asp |work=The Blue Book of Grammar and Punctuation |publisher=Jossey Bass |access-date=18 April 2014 |archive-date=19 April 2014 |archive-url=https://web.archive.org/web/20140419025523/http://www.grammarbook.com/punctuation/parens.asp |url-status=live}}</ref>

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 ([[Republican Party (United States)|R]]&nbsp;-&nbsp;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" (the slash in the second instance, as one alternative is replacing the other, not adding to it).

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]] 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 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]).

====Language====
A [[Parenthesis (rhetoric)|parenthesis in rhetoric]] and [[linguistics]] 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").<ref>{{cite dictionary |entry=Parenthesis |dictionary=The Oxford Dictionary of English Grammar |edition=2 |date=2014 |first=Bas |last=Aarts |publisher=Oxford University Press |isbn=978-0-191-74444-0}}</ref> 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{{snd}}What? Yes, that was her name!{{snd}}was my landlady" is also a parenthesis.<ref>{{cite dictionary |entry=Parenthesis |dictionary=The Concise Oxford Dictionary of Linguistics |edition=3 |date=2014 |first=P. H. |last=Matthews |publisher=Oxford University Press |isbn=978-0-191-75306-0}}</ref> (In non-specialist usage, the term "parenthetical phrase" is more widely understood.<ref>{{cite dictionary |entry=parenthetical |entry-url=http://www.thefreedictionary.com/parenthetical |title=The Free Online Dictionary |access-date=13 February 2013 |archive-date=6 June 2011 |archive-url=https://web.archive.org/web/20110606122628/http://www.thefreedictionary.com/parenthetical |url-status=live}}</ref>)

In [[phonetics]], parentheses are used for indistinguishable<ref name="IPA175">IPA ''Handbook'' p.&nbsp;175</ref> or unidentified utterances. They are also seen for silent articulation (mouthing),<ref name="IPA191">IPA ''Handbook'' p.&nbsp;191</ref> where the expected phonetic transcription is derived from lip-reading, and with periods to indicate silent pauses, for example {{IPA|(...)}} or {{IPA|(2 sec)}}.

====Enumerations====
An unpaired right parenthesis is often used as part of a label in an ordered list, such as this one:
{{blockquote|<poem>
a) [[education]]al testing,
b) technical writing and diagrams,
c) [[market research]], and
d) [[elections]].</poem>}}

====Accounting====
Traditionally in [[accounting]], contra amounts are placed in parentheses. A debit balance account in a series of credit balances will have parenthesis and vice versa.

====Parentheses in mathematics====
{{Main|Glossary of mathematical symbols#Parentheses|Bracket (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|4 × 3 + 2}} equals 14, since the [[multiplication]] is done before the [[addition]]. However, {{math|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:

{{bi|<math>[4 \times (3 + 2)]^2 = 400.</math>}}

====Parentheses in programming languages====
Parentheses are included in the syntaxes of many [[programming language]]s. 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 diagram]]s they are used for grouping, such as in [[extended Backus–Naur form]].

In Mathematica and the Wolfram language, parentheses are used to indicate grouping{{snd}}for 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 [[generic epithet|genus name]] and the [[specific epithet]].<ref>{{cite web |publisher=International Commission on Zoological Nomenclature |title=Names of subgenera |url=https://code.iczn.org/chapter-2-the-number-of-words-in-the-scientific-names-of-animals/article-6-interpolated-names/?frame=1 |website=International Code of Zoological Nomenclature |access-date=6 June 2021 |year=2012 |edition=4th |archive-date=7 June 2021 |archive-url=https://web.archive.org/web/20210607005720/https://code.iczn.org/chapter-2-the-number-of-words-in-the-scientific-names-of-animals/article-6-interpolated-names/?frame=1 |url-status=live}}</ref> For instance, ''Polyphylla'' (''Xerasiobia'') ''alba'' is a way to cite the species ''Polyphylla alba'' while also mentioning that it is in the subgenus ''Xerasiobia''.<ref>{{cite book |last1=Welter-Schultes |first1=Francisco W. |title=Guidelines for the Capture and Management of Digital Zoological Names Information |date=March 2013 |publisher=Global Biodiversity Information Facility |location=Copenhagen |isbn=9788792020444 |url=http://www.gbif.org/document/80625 |chapter=1.4.5.4 Species |pages=14–15}}</ref> 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 subgenus ''Xerasiobia'' within the genus ''Polyphylla''.<ref>{{cite book |last1=Welter-Schultes |first1=Francisco W. |title=Guidelines for the Capture and Management of Digital Zoological Names Information |date=March 2013 |publisher=Global Biodiversity Information Facility |location=Copenhagen |isbn=9788792020444 |url=http://www.gbif.org/document/80625 |chapter=1.4.5.3 Genera |page=14}}</ref> Parentheses are similarly used to cite a subgenus with the name of a [[prokaryotic]] species, although the [[International Code of Nomenclature of Prokaryotes]] (ICNP) requires the use of the abbreviation "subgen". as well, e.g., ''Acetobacter'' (subgen. ''Gluconoacetobacter'') ''liquefaciens''.<ref>{{cite journal |editor1-last=Parker |editor1-first=Charles T. |editor2-last=Tindall |editor2-first=Brian J. |editor3-last=Garrity |editor3-first=George M. |title=International Code of Nomenclature of Prokaryotes: Prokaryotic Code (2008 Revision) |journal=International Journal of Systematic and Evolutionary Microbiology |date=2019 |volume=69 |issue=1A |page=S19 |doi=10.1099/ijsem.0.000778 |pmid=26596770 |doi-access=free}}</ref>

====Chemistry====
Parentheses are used in [[chemistry]] to denote a repeated substructure within a molecule, e.g. HC(CH<sub>3</sub>)<sub>3</sub> ([[isobutane]]) or, similarly, to indicate the stoichiometry of ionic compounds with such substructures: e.g. Ca(NO<sub>3</sub>)<sub>2</sub> ([[calcium nitrate]]).

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 (e.g. in 3(AlO<sub>2</sub> + 2SO<sub>3</sub>) the 3 multiplies everything within the parentheses).{{sfn|Watts|1877|pp=140–141}}{{sfn|Ihde|1984|p=115}}

In [[chemical nomenclature]], parentheses are used to distinguish structural features and multipliers for clarity, for example in the polymer [[poly(methyl methacrylate)]].<ref>{{Cite web |title=R-0.1.5 Enclosing marks |url=https://www.acdlabs.com/iupac/nomenclature/93/r93_61.htm |access-date=3 May 2023 |website=ACDLabs.com |archive-date=3 May 2023 |archive-url=https://web.archive.org/web/20230503033434/https://www.acdlabs.com/iupac/nomenclature/93/r93_61.htm |url-status=live}}</ref>

{{clearright}}

==Square brackets<span class="anchor" id="square bracket"></span>==
{{Infobox punctuation mark
 |name     = Square brackets
 |variant1 = [&nbsp;]
 |unicode_list =
<div style="text-align:left;">
;General purpose{{br}}(half-width)<ref name="Basic Latin"/>:
:* {{unichar|005B|Left square bracket|html=}}
:* {{unichar|005D|Right square bracket|html=}}
;General purpose<br/>(full-width East Asian)<ref name="Halfwidth and Fullwidth Forms" />:
:* {{unichar|FF3B|Fullwidth left square bracket|html=}}
:* {{unichar|FF3D|Fullwidth right square bracket|html=}}
{{collapsible list|bullets=yes|title=[[Mediaeval studies]]<ref name="General Punctuation"/><ref name="Supplemental Punctuation" />
|{{unichar|2045|Left square bracket with quill|html=}}
|{{unichar|2046|Right square bracket with quill|html=}}
}}
{{collapsible list|bullets=yes|title=Technical/Mathematical<ref name="Unicode Miscellaneous Technical" /><ref name="Unicode Superscripts and Subscripts"/><ref name="Unicode Miscellaneous Mathematical Symbols-A"/><ref name="Unicode Miscellaneous Mathematical Symbols-B"/>
|{{unichar|23A1|Left square bracket upper corner|html=}}
|{{unichar|23A2|Left square bracket extension|html=}}
|{{unichar|23A3|Left square bracket lower corner|html=}}
|{{unichar|23A4|Right square bracket upper corner|html=}}
|{{unichar|23A5|Right square bracket extension|html=}}
|{{unichar|23A6|Right square bracket lower corner|html=}}
|{{unichar|23B4|Top square bracket|html=}}
|{{unichar|23B5|Bottom square bracket|html=}}
|{{unichar|23B6|Bottom square bracket over top square bracket|html=}}
|{{unichar|27E6|Mathematical left white square bracket|html=}}
|{{unichar|27E7|Mathematical right white square bracket|html=}}
|{{unichar|298B|Left square bracket with underbar|html=}}
|{{unichar|298C|Right square bracket with underbar|html=}}
|{{unichar|298D|Left square bracket with tick in top corner|html=}}
|{{unichar|2990|Right square bracket with tick in top corner|html=}}
|{{unichar|298E|Right square bracket with tick in bottom corner|html=}}
|{{unichar|298F|Left square bracket with tick in bottom corner|html=}}
}}
{{collapsible list|bullets=yes|title=Phonetic punctuation<ref name="Unicode Phonetic Punctuation"/>
|{{unichar|2E55|Left square bracket with stroke|html=}}
|{{unichar|2E56|Right square bracket with stroke|html=}}
|{{unichar|2E57|Left square bracket with double stroke|html=}}
|{{unichar|2E58|Right square bracket with double stroke|html=}}
}}
{{collapsible list|bullets=yes|title=Quotation<br />(East-Asian texts)<ref name="CJK Symbols and Punctuation"/>
|{{unichar|301A|Left white square bracket|html=}}
|{{unichar|301B|Right white square bracket|html=}}
}}
</div>
}}
{{Wiktionary pipe|square bracket||Unsupported titles/Square brackets|<nowiki>[&nbsp;]</nowiki>|Unsupported titles/Right square bracket|<nowiki>[</nowiki>|Unsupported titles/Left square bracket|<nowiki>]</nowiki>|crotchet|}}
{{char|[}} and {{char|]}} are ''square brackets'' in both British and American English, but are also more simply ''brackets'' in the latter.{{sfn|Pointon|Clark|2014|p=406}}{{sfn|McArthur|McArthur|2005}}
An older name for these brackets is "crotchets".<ref>Smith, John. ''The Printer's Grammar'' p. 84.</ref>

===Uses of [ ]<span class="anchor" id="Uses of square brackets"></span>===
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.<ref>{{cite book |title=The Chicago Manual of Style |edition=15th |publisher=[[University of Chicago Press]] |date=2003 |at=§6.104}}</ref> 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 an [[annotation]].<ref>{{cite book |title=California Style Manual |at=§4:59 |edition=4th}}</ref> For example: ''The Plaintiff asserted his cause is just, stating,''
{{blockquote|[m]y causes is [[sic|{{bracket|''sic''}}]] just.}}
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 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 |first=Kenneth G. |last=Wilson |work=The Columbia Guide to Standard American English |date=1993 |title=Brackets (Square, Angle) |publisher=Columbia University Press |via=Bartleby.com |archive-url= https://web.archive.org/web/20080524214802/http://www.bartleby.com/68/60/960.html |archive-date=24 May 2008}}</ref>
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 a [[wikt:verbose|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: "[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.<ref>{{cite book |title=The Chicago Manual of Style |edition=15th |publisher=[[University of Chicago Press]] |date=2003 |at=§6.102, §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".<ref>{{cite web |url= https://depts.washington.edu/engl/askbetty/changing_quotations.php |title=How to Integrate Direct Quotations into Your Writing |archive-url= https://web.archive.org/web/20210908042208/https://depts.washington.edu/engl/askbetty/changing_quotations.php |archive-date=8 September 2021 |publisher=University of Washington |date=2004 |work=Depts.Washington.edu}}</ref>

In translated works, brackets are used to signify the same word or phrase in the original language to avoid ambiguity.<ref>{{cite book |title=The Chicago Manual of Style |edition=15th |publisher=[[University of Chicago Press]] |date=2003 |at=§6.105}}</ref>
For example: ''He is trained in the way of the open hand [karate].''

[[Style guide|Style and usage guides]] originating in the [[News media#History|news industry of the twentieth century]], such as the ''[[AP Stylebook]]'', recommend against the use of square brackets because "They cannot be transmitted over [[List of wire services|news wires]]."<ref name="AP2014">{{cite encyclopedia |editor-last=Christian |editor-first=Darrell |editor-link=openlibrary:authors/OL7512788A |editor-last2=Froke |editor-first2=Paula Marie |editor-link2=openlibrary:authors/OL8932325A |editor-last3=Jacobsen |editor-first3=Sally A. |editor-link3=Sally Jacobsen |editor-last4=Minthorn |editor-first4=David |editor-link4=openlibrary:authors/OL7512789A |encyclopedia=[[AP Stylebook|Associated Press Stylebook]] 2014 |entry=brackets <nowiki>[]</nowiki> |version=Chapter "Punctuation Guide" |entry-url= https://archive.org/details/associatedpresss2014unse_l3a7/page/289/mode/1up |edition=49th |date=2014 |publisher=[[Associated Press]] |location=New York |isbn=9780917360589 |oclc=881182354 |lccn=2002249088 |page=289}}</ref> However, this guidance has little relevance outside of the technological constraints of the industry and era.

In linguistics, [[phonetic transcription]]s are generally enclosed within square brackets,<ref>{{cite book |title=The Chicago Manual of Style |edition=15th |publisher=[[University of Chicago Press]] |date=2003 |at=§6.107}}</ref> whereas [[phonemic]] transcriptions typically use paired [[Slash (punctuation)|slash]]es, according to [[International Phonetic Alphabet#Brackets and transcription delimiters|International Phonetic Alphabet]] rules. Pipes (|&nbsp;|) are often used to indicate a [[Morphophoneme|morphophonemic]] rather than phonemic representation. Other conventions are double slashes (⫽&nbsp;⫽), double pipes (‖&nbsp;‖) and curly brackets ({&nbsp;}).

In [[lexicography]], square brackets usually surround the section of a dictionary entry which contains the [[etymology]] of the word the entry defines.

====Proofreading====
Brackets (called ''move-left symbols'' or ''move right symbols'') are added to the sides of text in [[proofreading]] to indicate changes in indentation:

{| 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]]
|}

Square brackets are used to denote parts of the text that need to be checked when preparing drafts prior to finalizing a document.

====Law====
Square brackets are used in some countries in the citation of [[law report]]s to identify parallel citations to non-official reporters. For example:
{{blockquote|''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:
{{blockquote|''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:
{{blockquote|(1954) 98 Sol Jo 176}}
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====
{{main|Glossary of mathematical symbols#Square brackets}}
Brackets are used in [[mathematics]] in a variety of notations, including standard notations for [[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 be used exclusively or in combination with parentheses to represent [[interval (mathematics)|interval]]s as ''interval notation''.{{sfn|Achatz|Anderson|2005|pp=165&ndash;166}} For example, {{math|[0,5]}} represents the set of real numbers from 0 to 5 inclusive. Both parentheses and brackets are used to denote a ''half-open'' interval; {{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, but 12.0 is not included. In some European countries, the notation {{math|[5, 12[}} is also used.<ref>{{Cite web |title=Halboffenes Intervall |url=https://www.mathe-lexikon.at/mengenlehre/intervalle/halboffenes-intervall.html |access-date=2024-04-20 |website=www.mathe-lexikon.at |language=de}}</ref><ref>{{Cite web |title=Intervall Mathe • alle Arten & Schreibweisen |url=https://studyflix.de/mathematik/intervall-mathe-4398 |access-date=2024-04-20 |website=Studyflix |language=de}}</ref> The endpoint adjoining the square bracket is known as ''closed'', whereas the endpoint adjoining the parenthesis is known as ''open''.{{sfn|Achatz|Anderson|2005|pp=165&ndash;166}}

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}} }}.

====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 (particularly distributed charge in a [[Complex (chemistry)|complex ion]]), repeating chemical units (particularly in polymers) and transition state structures, among other uses.

====Square brackets in programming languages====
Brackets are used in many computer [[programming language]]s, primarily for [[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. In [[syntax diagram]]s they are used for optional portions, such as in [[extended Backus–Naur form]].

===Double brackets ⟦ ⟧<span class="anchor" id="Double brackets"></span>===
Double brackets (or white square brackets or [[Dana Scott|Scott]] brackets), ⟦&nbsp;⟧, 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>{{cite book |last1=Scott |first1=D. |last2=Strachey |first2=C. |date=1971 |title=Toward a Mathematical Semantics for Computer Languages |publisher=Oxford University Computing Laboratory, Programming Research Group}}</ref>  In the [[Wolfram Language]], double brackets, either as iterated single brackets ({{not a typo|&lsqb;&lsqb;}}) or ligatures (〚) are used for [[Array index|list indexing]].<ref>{{cite web |publisher=Wolfram Research |title=Part, Wolfram Language function |work=Reference.Wolfram.com |date=2014 |orig-year=1988 |url= https://reference.wolfram.com/language/ref/Part.html |archive-url= https://web.archive.org/web/20230331205319/https://reference.wolfram.com/language/ref/Part.html |archive-date=31 March 2023 |quote=In StandardForm and InputForm, ''expr''{{brackets|''spec''}} can be input as ''expr''〚''spec''〛.}}</ref>

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 [[Interval (mathematics)#Integer intervals|intervals of integers]] or, less often, the [[Floor and ceiling functions|floor function]]. In papyrology, following the [[Leiden Conventions]], they are used to enclose text that has been deleted in antiquity.<ref>{{Cite web |url= http://papyri.info/docs/leiden_plus#leiden-double-square-brackets-- |website=Papyri.info |title=Text Leiden+ Documentation |access-date=5 March 2020 |archive-date=24 February 2020 |archive-url= https://web.archive.org/web/20200224062541/http://papyri.info/docs/leiden_plus#leiden-double-square-brackets-- |url-status=live}}</ref>

===Lenticular brackets【】<span class="anchor" id="Lenticular brackets"></span>===
{{Wiktionary|【&nbsp;】}}
Some [[East Asia]]n languages use lenticular brackets {{Char|【}} {{Char|】}}, a combination of square brackets and round brackets called {{linktext|lang=zh|方頭括號}} (''fāngtóu kuòhào'') in [[Chinese language|Chinese]] and {{lang|ja|
隅付き括弧}} (''sumitsuki kakko'') in [[Japanese language|Japanese]]. They are used in titles and headings in both Chinese<ref>{{citation |title=GB/T 15834-2011 标点符号用法 (General rules for punctuation) |date=10 December 2011 |at=4.9.3.3, 4.9.3.5}}</ref> 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.

===Floor ⌊ ⌋ and ceiling ⌈ ⌉ corner brackets<span class="anchor" id="Floor and ceiling corner brackets"></span>===
{{Infobox punctuation mark
 |name     = Floor and ceiling
 |variant1 = ⌈''ceiling''⌉
 |variant2 = ⌊''floor''⌋
 |unicode_list =
<div style="text-align:left;">
;[[Floor and ceiling functions]]<ref name="Unicode Miscellaneous Technical"/>:
:* {{unichar|2308|Left ceiling|html=}}
:* {{unichar|2309|Right ceiling|html=}}
:* {{unichar|230A|Left floor|html=}}
:* {{unichar|230B|Right floor|html=}}
</div>
}}
{{Wiktionary|⌊&nbsp;⌋|⌈&nbsp;⌉}}
The floor corner brackets {{char|⌊}} and {{char|⌋}}, the ceiling corner brackets {{char|⌈}} and {{char|⌉}} (U+2308, U+2309) are used to denote the integer [[floor and ceiling functions]].

===Quine corners ⌜⌝ and half brackets ⸤ ⸥ or ⸢ ⸣<span class="anchor" id="Quine corners and half brackets"></span>===
The Quine corners {{char|⌜}} and {{char|⌝}} have at least two uses in [[mathematical logic]]: either as [[quasi-quotation]], a generalization of quotation marks, or to denote the [[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" />

===Brackets with quills ⁅ ⁆<span class="anchor" id="Brackets with quills"></span>===
Known as "spike parentheses" ({{langx|sv|piggparenteser}}), {{code|⁅}} and {{code|⁆}} are used in Swedish [[bilingual dictionary|bilingual dictionaries]] to enclose supplemental constructions.<ref>Examples may be found under the corresponding entry at [[:sv:Parentes#Piggparenteser ⁅ ⁆|:sv:Parentes]].</ref>

{{clear}}

==Curly brackets<span class="anchor" id="Braces"></span><span class="anchor" id="Brace"></span><span class="anchor" id="Curly bracket"></span>==
{{Infobox punctuation mark
 |name     = Curly brackets
 |variant1 = {&nbsp;}
 |unicode_list =
<div style="text-align:left;">
;General<br/>(half width)<ref name="Basic Latin" />:
:* {{unichar|007B|Left curly bracket|html=}}
:* {{unichar|007D|Right curly bracket|html=}}
;General<br/>(full-width East Asian)<ref name="Halfwidth and Fullwidth Forms" />:
:* {{unichar|FF5B|Fullwidth left curly bracket|html=}}
:* {{unichar|FF5D|Fullwidth right curly bracket|html=}}
{{collapsible list|bullets=yes|title=Technical/Mathematical<br/>(half-width)<ref name="Unicode Miscellaneous Technical" /><ref name="Unicode Superscripts and Subscripts"/><ref name="Unicode Miscellaneous Mathematical Symbols-A"/><ref name="Unicode Miscellaneous Mathematical Symbols-B"/>
|{{unichar|23A7|Left curly bracket upper hook|html=}}
|{{unichar|23A8|Left curly bracket middle piece|html=}}
|{{unichar|23A9|Left curly bracket lower hook|html=}}
|{{unichar|23AB|Right curly bracket upper hook|html=}}
|{{unichar|23AC|Right curly bracket middle piece|html=}}
|{{unichar|23AD|Right curly bracket lower hook|html=}}
|{{unichar|23AA|Curly bracket extension|html=}}
|{{unichar|23B0|Upper left or lower right curly bracket section|html=}}
|{{unichar|23B1|Upper right or lower left curly bracket section|html=}}
|{{unichar|23DE|Top curly bracket|html=}}
|{{unichar|23DF|Bottom curly bracket|html=}}
}}
{{collapsible list|bullets=yes|title=[[Dingbat]]s<ref name="Unicode Dingbats"/>
|{{unichar|2774|Medium left curly bracket ornament|html=}}
|{{unichar|2775|Medium right curly bracket ornament|html=}}
}}
</div>
}}
{{char|&lbrace;}} and {{char|&rbrace;}} are ''curly brackets'' or ''braces'' in both American and British English.{{sfn|Pointon|Clark|2014|p=406}}{{sfn|McArthur|McArthur|2005}}

===Uses of { }<span class="anchor" id="Uses of curly brackets"></span>===
[[File:Curly Bracket Notation.png|thumb|upright=0.5|left|An example of curly brackets used to group sentences together]]
Curly brackets are used by text editors to mark editorial insertions<ref>{{cite book |url=https://books.google.com/books?id=ypA27dtL0-oC&pg=PA6 |page=6 |title=Medieval Hebrew Poetry in Muslim Egypt: The Secular Poetry of the Karaite Poet Moses Ben Abraham Dar'i |series=Karaite Texts and Studies |volume=3 |editor1-first=Joachim J.M.S. |editor1-last=Yeshaya |publisher=Brill |year=2010 |isbn=9789004191303}}</ref> or interpolations.<ref>{{cite book |url=https://books.google.com/books?id=9yG9ZB0waQsC&pg=PA1053 |page=1053 |title=Textual Evidence and Commentary |volume=5 |series=The Collected Poetry of Robinson Jeffers |editor1-first=Tim |editor1-last=Hunt |publisher=Stanford University Press |year=1988 |isbn=9780804738170}}</ref>

Braces used to be used to connect multiple lines of poetry, such as triplets in a poem of rhyming [[couplet]]s,<ref>{{cite book |url=https://books.google.com/books?id=0eRtOqjNMxEC&pg=PA122 |page=122 |title=The Poetry Handbook |first=John |last=Lennard |edition=2 |publisher=Oxford University Press |location=Oxford |year=2006 |isbn=9780191532733}}</ref> although this usage had gone out of fashion by the 19th century.{{sfn|Robertson|1785|p=143}}{{sfn|Wilson|1850|p=165}}

Another older use in prose was to eliminate duplication in lists and tables.{{sfn|Wilson|1850|p=165}}
Two examples here from [[Charles Hutton]]'s 19th century table table of weights and measures in his ''A Course of Mathematics'':
<blockquote style="border:1px solid; padding:0.5em;">
{| cellpadding=0; cellspacing=0;
|+ In this kingdom{{sfn|Hutton|1836|p=18}}
|-
| rowspan="5" | The standard of ... || ⎧ || Length is a Yard.
|-
| ⎪ || Surface is a Square Yard, the {{frac|1|4840}} of an Acre.
|-
| ⎨ || ⎰ Solidity is a Cubic Yard.
|-
| ⎪ || ⎱ Capacity is a Gallon.
|-
| ⎩ || Weight is a Pound.
|}
</blockquote>
<blockquote style="border:1px solid; padding:0.5em;">
{| cellpadding=0; cellspacing=0;
|+ Imperial measure of CAPACITY for coals, culm, lime, fish, potatoes, fruit,&ndash; and other goods commonly sold by ''heaped measure'':{{sfn|Hutton|1836|p=20}}
|-
| 2 Gallons || = 1 Peck || = 764 || ⎱
| rowspan = "2" | Cubic Inches, nearly
|-
| 8 Gallons || = 1 Bushel || = {{frac|2813|1|2}} || ⎰
|-
| 3 Bushels || = 1 Sack || = {{frac|4|8|9}} || ⎱
| rowspan = "2" | Cubic Feet, nearly
|-
| 12 Sacks || = 1 Chald. || = {{frac|58|2|3}} || ⎰
|}
</blockquote>

As an extension to the [[International Phonetic Alphabet]] (IPA), [[International Phonetic Alphabet#Brackets and transcription delimiters|braces are used for prosodic notation]].

====Music====
In music, they are known as "[[Accolade (notation)|accolades]]" or "[[Brace (music)|braces]]", and connect two or more lines (staves) of music that are played simultaneously.<ref>{{cite web |url= http://www.decodeunicode.org/u%2B007B |title=U+007B LEFT CURLY BRACKET |website=DecodeUnicode.org |access-date=3 May 2009 |archive-url= https://web.archive.org/web/20081202121802/http://www.decodeunicode.org/u%2B007B |archive-date=2 December 2008}}</ref>

==== Chemistry ====
The use of braces in chemistry is an old notation that has long since been superseded by subscripted numbers.{{sfn|Watts|1877|pp=140&ndash;141}}
The chemical formula for water, H<sub>2</sub>O, was represented as <math>\left . {{H}\atop{H}} \right \} O</math>.{{sfn|Watts|1877|pp=140&ndash;141}}

{{clearleft}}

====Curly brackets in programming languages====
{{See also|Bracing style}}
In many programming languages, curly brackets enclose groups of [[Statement (programming)|statement]]s and create a local [[Scope (computer science)|scope]]. Such languages ([[C (programming language)|C]], C#, C++ and many others) 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=Programming with Style |via=Riedquat.de |archive-url= https://web.archive.org/web/20150924070732/http://www.riedquat.de/prog/style |archive-date=24 September 2015}}</ref> They are also used to define structures and [[enumerated type]] in these languages.

In various [[Unix shell]]s, 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.{{sfn|Newham|Rosenblatt|1998|p=14}}
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.{{sfn|Sobell|Seebach|2005|p=323}}

In [[syntax diagram]]s they are used for repetition, such as in [[extended Backus–Naur form]].

In the [[Z notation|Z]] [[formal specification]] language, braces define a set.

====Curly brackets in mathematics====
{{main|Glossary of mathematical symbols#Braces}}
In [[mathematics]] they delimit [[Set (mathematics)|set]]s, in what is called ''set notation''.{{sfn|Biggs|2002}}
Braces enclose either a literal list of set elements, or a rule that defines the set elements.{{sfn|Biggs|2002}}
For example:
*{{math|1=S = <nowiki>{</nowiki>{{mvar|a}}, {{mvar|b}}<nowiki>}</nowiki>}} defines a set {{mvar|S}} containing {{mvar|a}} and {{mvar|b}}.{{sfn|Biggs|2002}}
*{{math|1=S = <nowiki>{</nowiki>{{mvar|x}} <nowiki>|</nowiki> {{mvar|x}} &gt; 0<nowiki>}</nowiki>}} defines a set {{mvar|S}} containing elements (implied to be numbers) {{math|{{mvar|x}}<sub>0</sub>}}, {{math|{{mvar|x}}<sub>1</sub>}}, and so on where every {{math|{{mvar|x}}<sub>{{mvar|n}}</sub>}} satisfies the rule that it is greater than zero.{{sfn|Biggs|2002}}

They are often also used to denote the [[Poisson bracket]] between two quantities.

In [[ring theory]], braces denote the [[anticommutator]] where {{math|<nowiki>{</nowiki>{{mvar|a}}, {{mvar|b}}<nowiki>}</nowiki>}} is defined as {{math|{{mvar|a}} {{mvar|b}} + {{mvar|b}} {{mvar|a}} }}.

{{Wiktionary pipe|curly bracket||brace||Unsupported&nbsp;titles/Curly brackets|<nowiki>{&nbsp;}</nowiki>|Unsupported&nbsp;titles/Right curly bracket|<nowiki>{</nowiki>|Unsupported&nbsp;titles/Left curly bracket|<nowiki>}</nowiki>|squiggly||accolade|}}
{{clear}}

==Angle brackets<span class="anchor" id="Angle bracket"></span><span class="anchor" id="Chevrons"></span><span class="anchor" id="Chevron"></span>==
{{Redirect|Angle bracket|a mechanical part used for joining|Angle bracket (fastener)}}
{{More citations needed section|date=November 2012}}
{{Infobox punctuation mark
 |name     = Angle brackets
 |variant1 = ⟨&nbsp;⟩
 |caption1 = Angle brackets (BE&AE){{sfn|Pointon|Clark|2014|p=406}}
 |variant2 = ⟪&nbsp;⟫
 |caption2 = Angle brackets (BE&AE){{sfn|Pointon|Clark|2014|p=406}}
 |variant3 = &lt;&nbsp;&gt;
 |caption3 = less-than and greater-than
 |unicode_list =
<div style="text-align:left;">
;Less/greater than<br/>(half width)<ref name="Basic Latin" />:
:* {{unichar|003C|Less-than sign|html=}}
:* {{unichar|003E|Greater-than sign|html=}}
;Less/greater than<br/>(full-width East Asian)<ref name="Halfwidth and Fullwidth Forms" />:
:*{{unichar|FF1C|Fullwidth less-than sign|html=}}
:*{{unichar|FF1E|Fullwidth greater-than sign|html=}}
{{collapsible list|bullets=yes|title=Technical/Mathematical<br/>(half-width)<ref name="Unicode Miscellaneous Technical" /><ref name="Unicode Superscripts and Subscripts"/><ref name="Unicode Miscellaneous Mathematical Symbols-A"/><ref name="Unicode Miscellaneous Mathematical Symbols-B"/>
|{{unichar|2329|Left-pointing angle bracket|html=}}{{efn|name=lang-rang}}
|{{unichar|232A|Right-pointing angle bracket|html=}}{{efn|name=lang-rang}}
|{{unichar|27E8|Mathematical left angle bracket|html=}}{{efn|name=lang-rang}}
|{{unichar|27E9|Mathematical right angle bracket|html=}}{{efn|name=lang-rang}}
|{{unichar|27EA|Mathematical left double angle bracket|html=}}
|{{unichar|27EB|Mathematical right double angle bracket|html=}}
|{{unichar|2991|Left angle bracket with dot|html=}}
|{{unichar|2992|Right angle bracket with dot|html=}}
|{{unichar|29FC|Left-pointing curved angle bracket|html=}}
|{{unichar|29FD|Right-pointing curved angle bracket|html=}}
}}
{{collapsible list|bullets=yes|title=Quotation<br />(fullwidth East-Asian texts)<ref name="CJK Symbols and Punctuation"/>
|{{unichar|3008|Left angle bracket|html=}}
|{{unichar|3009|Right angle bracket|html=}}
|{{unichar|300A|Left double angle bracket|html=}}
|{{unichar|300B|Right double angle bracket|html=}}
}}
{{collapsible list|bullets=yes|title=[[Dingbat]]s<ref name="Unicode Dingbats"/>
|{{unichar|276C|Medium left-pointing angle bracket ornament|html=}}
|{{unichar|276D|Medium right-pointing angle bracket ornament|html=}}
|{{unichar|2770|Heavy left-pointing angle bracket ornament|html=}}
|{{unichar|2771|Heavy right-pointing angle bracket ornament|html=}}
|{{unichar|276E|Heavy left-pointing angle quotation mark ornament|html=}}
|{{unichar|276F|Heavy right-pointing angle quotation mark ornament|html=}}
}}
</div>
}}

{{char|&lang;}} and {{char|&rang;}} are ''angle brackets'' in both American and British English.{{sfn|Pointon|Clark|2014|p=406}}{{sfn|McArthur|McArthur|2005}} In computer slang, they are known as "brokets".<ref name="brocket">{{cite web |url= http://catb.org/jargon/html/B/broket.html |title=broket |work=[[The Jargon File]] |edition=ver. 4.4.7 |last1=Raymond |first1=Eric S. |via=CatB.org |access-date=13 February 2013 |archive-date=10 February 2013 |archive-url= https://web.archive.org/web/20130210033248/http://www.catb.org/jargon/html/B/broket.html |url-status=live}}</ref>

Strictly speaking they are distinct from V-shaped ''chevrons'', as they have (where the typography permits it) a broader span than chevrons,{{sfn|Peters|2007|p=138}} although when printed often no visual distinction is made.{{sfn|Peters|2007|p=101}}

The ASCII less-than and greater-than characters {{tt|<>}} are often used for angle brackets. In most cases only those characters are accepted by computer programs, and the Unicode angle brackets are not recognized (for instance, in [[HTML tag]]s). The characters for "single" [[guillemet]]s {{tt|‹›}} are also often used, and sometimes normal guillemets {{tt|«»}} when nested angle brackets are needed.

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.

{{notelist|refs=
<ref name="lang-rang">&amp;lang; and &amp;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] ({{Webarchive|url= https://web.archive.org/web/20130127173609/http://www.w3.org/TR/xml-entity-names/#diff-xhtml1 |date=27 January 2013}}).</ref>
}}

===Shape===
Angle brackets are larger than [[less-than sign|less-than]] and [[greater-than sign]]s, which in turn are larger than [[guillemet]]s.

[[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 [[guillemet]]s in fonts [[Cambria (typeface)|Cambria]], [[DejaVu fonts|DejaVu]] Serif, [[Andron (typeface)|Andron]] Mega Corpus, [[Andika (typeface)|Andika]] and [[Everson Mono]]]]
{{clearleft}}
===Uses of ⟨ ⟩<span class="anchor" id="Uses of angle brackets"></span>===
Angle brackets are infrequently used to denote [[Intrapersonal communication|words that are thought]] instead of spoken, such as:

:{{angbr|What an unusual flower!}}

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]] |page=22 |chapter-url=https://books.google.com/books?id=EHeGzQ8wuLQC&pg=PA22 |chapter=Angle brackets |isbn=9781579582180 |access-date=8 August 2015 |archive-date=31 October 2023 |archive-url=https://web.archive.org/web/20231031135122/https://books.google.com/books?id=EHeGzQ8wuLQC&pg=PA22#v=onepage&q&f=false |url-status=live }}</ref>

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. Since no foreign language is actually written, this is only ''notionally'' translated.{{Citation needed|date=March 2017}}

In [[linguistics]], angle brackets identify [[grapheme]]s ({{abbr|e.g.|for example}}, letters of an alphabet) or [[orthography]], as in "The English word {{IPA|/kæt/}} is spelled {{angbr|cat}}."<ref>{{cite book |last=Bauer |first=Laurie |title=The Linguistics Student's Handbook |date=2007 |publisher=[[Edinburgh University Press]] |page=99 |chapter-url=https://books.google.com/books?id=WsrtrmHkLvoC&pg=PA99 |chapter=Notational conventions: Brackets |isbn=9780748627592 |access-date=8 August 2015 |archive-date=31 October 2023 |archive-url=https://web.archive.org/web/20231031135124/https://books.google.com/books?id=WsrtrmHkLvoC&pg=PA99 |url-status=live }}</ref><ref name="Sampson">{{cite book |last=Sampson |first=Geoffrey |editor-last=Allan |editor-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 |isbn=9781317513049 |access-date=8 August 2015 |archive-date=31 October 2023 |archive-url=https://web.archive.org/web/20231031135126/https://books.google.com/books?id=3vssCgAAQBAJ&pg=PA60#v=onepage&q&f=false |url-status=live }}</ref><ref name="Trask" /> {{crossref|(See [[International Phonetic Alphabet#Brackets and transcription delimiters|IPA Brackets and transcription delimiters]].)}}

In [[epigraphy]], they may be used for mechanical transliterations of a text into the Latin script.<ref name="Sampson" />

In [[Quotation mark#Chinese, Japanese and Korean quotation marks|East Asian punctuation]], angle brackets are used as [[quotation mark]]s. Chevron-like symbols are part of standard [[Chinese language|Chinese]], [[Japanese language|Japanese]] and{{snd}} less frequently{{snd}} [[Korean language|Korean]] punctuation, where they generally enclose the titles of books, as: <span style="writing-mode:vertical-rl">〈 ... 〉</span> or <span style="writing-mode:vertical-rl">《 ... 》</span> for traditional [[tategaki|vertical printing]] — written in vertical lines — and as 〈 ... 〉 or 《 ... 》 for [[yokogaki|horizontal]] printing — in horizontal.

====Angle brackets in mathematics====
{{main|Glossary of mathematical symbols#⟨⟩}}
Angle brackets (or 'chevrons') are used in [[group theory]] to write [[group presentation]]s, and to denote the [[group generators|subgroup generated]] by a collection of elements. In [[set theory]], chevrons or parentheses are used to denote [[ordered pair]]s<ref>{{cite book |last=Hefferon |first=Jim |title=Linear algebra |edition=Third |url= http://joshua.smcvt.edu/linearalgebra/book_ed3.pdf |page=121 |publisher=Saint Michael's College |access-date=26 March 2021 |archive-date=3 December 2020 |archive-url= https://web.archive.org/web/20201203193951/http://joshua.smcvt.edu/linearalgebra/book_ed3.pdf |url-status=live}}</ref> and other [[tuple]]s, 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 (''[[Expected value#Notations|expected value]]'') 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>

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]]'', to note vectors from the [[dual space]]s of the Bra&nbsp;{{angbr|{{math|''A''{{pipe}}}} and the Ket&nbsp;{{math|{{pipe}}''B''}}}}. But there are [[Inner product space#Alternative definitions, notations and remarks|other notations]] used.

In [[continuum mechanics]], chevrons may be used as [[Macaulay brackets]].

====Angle brackets in programming languages====
In [[C++]] chevrons (actually less-than and greater-than) are used to surround arguments to [[template (C++)|template]]s. They are also used to surround the names of [[header file#C/C++|header files]]; this usage was inherited from and is also found in [[C (programming language)|C]].

In the [[Z notation|Z]] [[formal specification]] language, chevrons define a sequence.

In [[HTML]], chevrons (actually 'greater than' and 'less than' symbols) are used to bracket meta text. For example {{tag|b|o}} 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 {{tag|b|c}}. This use is sometimes extended as an informal mechanism for communicating mood or tone in digital formats such as messaging, for example adding "&lt;sighs&gt;" at the end of a sentence.

{{Wiktionary pipe|angle bracket||⟨&nbsp;⟩||Unsupported titles/Enclosing less than greater than|<&nbsp;>|broket||pointy bracket||diamond bracket|}}
{{clear}}

==Unicode<span class="anchor" id="Encoding"></span>==
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.

{|class="wikitable"
|+Unicode and HTML encodings for various bracket characters
|-
!scope="col"| Uses!!scope="col"| Unicode/HTML !!scope="col"| Sample
<!-- Quotation marks are not brackets, see ==List of types==-->
|-
|rowspan="4"| [[quasi-quotation|Quine corners]]<ref name="Unicode Miscellaneous Technical" />
| {{unichar|231C|html=}}||rowspan="2"| ⌜''quasi-quotation''⌝<br />⌜''editorial notation''⌝
|-
| {{unichar|231D|html=}}
|-
| {{unichar|231E|html=}} ||rowspan="2"| ⌞''editorial notation''⌟
|-
| {{unichar|231F|html=}}
|-
|rowspan="2"| Fullwidth parentheses<ref name="Halfwidth and Fullwidth Forms" />
| {{unichar|FF5F|html=}} ||rowspan="2"| ｟...｠
|-
| {{unichar|FF60|html=}}
|-
|rowspan="24"| Technical/mathematical<br />(specialized)<ref name="Unicode Miscellaneous Technical" /><ref name="Unicode Superscripts and Subscripts"/><ref name="Unicode Miscellaneous Mathematical Symbols-A"/><ref name="Unicode Miscellaneous Mathematical Symbols-B"/>
| {{unichar|23B8|html=}}||rowspan="2"|⎸boxed text⎹
|-
| {{unichar|23B9|html=}}
|-
| {{unichar|23E0|html=}} ||rowspan="2" style="line-height: 1 !important; text-align: center;"|
⏠<br />
tortoise shell brackets<br />
⏡
|-
| {{unichar|23E1|html=}}
|-
| {{unichar|27C5|html=}} ||rowspan="2"| ⟅...⟆
|-
| {{unichar|27C6|html=}}
|-
| {{unichar|27D3|html=}} ||rowspan="2"| ⟓pullback...pushout⟔
|-
| {{unichar|27D4|html=}}
|-
| {{unichar|27EC|html=}}||rowspan="2"| ⟬white tortoise shell brackets⟭
|-
| {{unichar|27ED|html=}}
|-
| {{unichar|2987|html=}}||rowspan="2"| ''{{math|R}}''⦇''{{math|S}}''⦈
|-
| {{unichar|2988|html=}}
|-
| {{unichar|2989|html=}}||rowspan="2"| ⦉{{math|''x'':'''Z'''}}⦊
|-
| {{unichar|298A|html=}}
|-
| {{unichar|2993|html=}}||rowspan="2"| ⦓[[Inequality (mathematics)|inequality]] sign brackets⦔
|-
| {{unichar|2994|html=}}
|-
| {{unichar|2995|html=}}||rowspan="2"| ⦕inequality sign brackets⦖
|-
| {{unichar|2996|html=}}
|-
| {{unichar|2997|html=}}||rowspan="2"| ⦗black tortoise shell brackets⦘
|-
| {{unichar|2998|html=}}
|-
| {{unichar|29D8 |html=}}||rowspan="2"| ⧘...⧙
|-
| {{unichar|29D9|html=}}
|-
| {{unichar|29DA|html=}} ||rowspan="2"| ⧚...⧛
|-
| {{unichar|29DB|html=}}
|-
|rowspan="4"| Half brackets<ref name="Supplemental Punctuation"/>
| {{unichar|2E22|html=}}||rowspan="2"| ⸢''editorial notation''⸣
|-
| {{unichar|2E23 |html=}}
|-
| {{unichar|2E24|html=}}||rowspan="2"| ⸤''editorial notation''⸥
|-
| {{unichar|2E25|html=}}
|-
|rowspan="6"| [[Small Form Variants|Compatibility variants for CNS 11643]]<ref name="Small Form Variants"/>
| {{unichar|FE59|html=}} ||rowspan="2"| ﹙...﹚
|-
| {{unichar|FE5A|html=}}
|-
| {{unichar|FE5B |html=}} ||rowspan="2"| ﹛...﹜
|-
| {{unichar|FE5C|html=}}
|-
| {{unichar|FE5D|html=}} ||rowspan="2"| ﹝...﹞
|-
| {{unichar|FE5E |html=}}
|-
|rowspan="2"| [[Dingbat]]s<ref name="Unicode Dingbats"/>
| {{unichar|2772|html=}} ||rowspan="2"| ❲light tortoise shell bracket ornament❳
|-
| {{unichar|2773|html=}}
|-
|rowspan="2"| [[N'Ko alphabet|N'Ko]]<ref name="Supplemental Punctuation" />
| {{unichar|2E1C|html=}} ||rowspan="2"| {{script|Nkoo|⸜ߒߞߏ⸝}}
|-
| {{unichar|2E1D|html=}}
|-
|rowspan="2"| [[Ogham]]<ref name="Uncode Ogham">{{cite web |url= https://www.unicode.org/charts/PDF/U1680.pdf |title=Ogham Code Chart |work=The Unicode Standard |publisher=Unicode Consortium |access-date=7 February 2016 |archive-date=12 August 2021 |archive-url= https://web.archive.org/web/20210812013616/https://www.unicode.org/charts/PDF/U1680.pdf |url-status=live}}</ref>
| {{unichar|169B|html=}}||rowspan="2"| <big>᚛ᚑᚌᚐᚋ᚜</big>
|-
| {{unichar|169C|html=}}
|-
| [[Old Hungarian alphabet|Old Hungarian]] || {{unichar|2E42|html=}}|| ⹂
|-
|rowspan="4"| [[Tibetan alphabet|Tibetan]]<ref name="Unicode Tibetan">{{cite web |url= https://www.unicode.org/charts/PDF/U0F00.pdf |title=Tibetan Code Chart |work=The Unicode Standard |publisher=Unicode Consortium |access-date=7 February 2016 |archive-date=13 April 2018 |archive-url= https://web.archive.org/web/20180413024814/http://www.unicode.org/charts/PDF/U0F00.pdf |url-status=live}}</ref>
| {{unichar|0F3A |html=}} ||rowspan="2"| <big>༺དབུ་ཅན་༻</big>
|-
| {{unichar|0F3B |html=}}
|-
| {{unichar|0F3C|html=}}||rowspan="2"| <big>༼༡༢༣༽</big>
|-
| {{unichar|0F3D |html=}}
|-
|rowspan="8"| [[New Testament]] editorial marks<ref name="Supplemental Punctuation" />
| {{unichar|2E02 |html=}}||rowspan="2"| ⸂...⸃
|-
| {{unichar|2E03 |html=}}
|-
| {{unichar|2E04 |html=}} ||rowspan="2"| ⸄...⸅
|-
| {{unichar|2E05|html=}}
|-
| {{unichar|2E09|html=}}||rowspan="2"| ⸉...⸊
|-
| {{unichar|2E0A |html=}}
|-
| {{unichar|2E0C|html=}}||rowspan="2"| ⸌...⸍
|-
| {{unichar|2E0D|html=}} 
|-
|rowspan="2"| [[Medieval studies]]<ref name="General Punctuation"/><ref name="Supplemental Punctuation" />
| {{unichar|2E26|html=}} ||rowspan="2"| ⸦crux⸧
|-
| {{unichar|2E27|html=}}
|-
|rowspan="8"| Quotation<br />(East-Asian texts)<ref name="CJK Symbols and Punctuation" />
| {{unichar|3014 |html=}}||rowspan="2"| 〔...〕
|-
| {{unichar|3015 |html=}}
|-
| {{unichar|3016|html=}} ||rowspan="2"| 〖...〗
|-
| {{unichar|3017 |html=}}
|-
| {{unichar|3018 |html=}} ||rowspan="2"| 〘...〙
|-
| {{unichar|3019 |html=}} 
|-
| {{unichar|301D |html=}}  ||rowspan="2"| 〝...〞
|-
| {{unichar|301E |html=}}{{efn|name=301E}} 
|-
| rowspan="2" |Quotation<br />([[halfwidth and fullwidth forms|halfwidth]] East-Asian texts)<ref name="Unicode Miscellaneous Technical" /><ref name="Halfwidth and Fullwidth Forms" />
| {{unichar|FF62 |html=}}|| rowspan="2" | ｢ｶﾀｶﾅ｣
|-
| {{unichar|FF63 |html=}}
|-
|rowspan="6"| Quotation<br />(fullwidth East-Asian texts)<ref name="CJK Symbols and Punctuation"/>
| {{unichar|300C|html=}}  ||rowspan="2"| 「表題」
|-
| {{unichar|300D|html=}}
|-
| {{unichar|300E |html=}} ||rowspan="2"| 『表題』
|-
| {{unichar|300F |html=}}
|-
| {{unichar|3010 |html=}}  ||rowspan="2"| 【表題】
|-
| {{unichar|3011 |html=}}
|-
|rowspan="20"| Vertical bracket presentation forms<ref name="CJK Compatibility Forms"/><ref name="Vertical Forms"/>{{efn|name=Vertical presentation forms}}
| {{unichar|FE17 |html=}}  ||rowspan="2" style="writing-mode: vertical-rl;"| ︗...︘
|-
| {{unichar|FE18|html=|alias=yes}}{{efn|name=FE18}}
|-
| {{unichar|FE35|html=}}||rowspan="2" style="writing-mode: vertical-rl;"| ︵...︶
|-
| {{unichar|FE36 |html=}}
|-
| {{unichar|FE37|html=}}||rowspan="2" style="writing-mode: vertical-rl;"| ︷...︸
|-
| {{unichar|FE38|html=}}
|-
| {{unichar|FE39|html=}} ||rowspan="2" style="writing-mode: vertical-rl;"| ︹...︺
|-
| {{unichar|FE3A |html=}}
|-
| {{unichar|FE3B |html=}}  ||rowspan="2" style="writing-mode: vertical-rl;"| ︻...︼
|-
| {{unichar|FE3C |html=}}
|-
| {{unichar|FE3D |html=}}  ||rowspan="2" style="writing-mode: vertical-rl;"| ︽...︾
|-
| {{unichar|FE3E |html=}} 
|-
| {{unichar|FE3F |html=}}  ||rowspan="2" style="writing-mode: vertical-rl;"| ︿...﹀
|-
| {{unichar|FE40 |html=}}
|-
| {{unichar|FE41|html=}} ||rowspan="2" style="writing-mode: vertical-rl;"| ﹁...﹂
|-
| {{unichar|FE42|html=}}
|-
| {{unichar|FE43 |html=}}  ||rowspan="2" style="writing-mode: vertical-rl;"| ﹃...﹄
|-
| {{unichar|FE44 |html=}}
|-
| {{unichar|FE47 |html=}}  ||rowspan="2" style="writing-mode: vertical-rl;"| ﹇...﹈
|-
| {{unichar|FE48 |html=}}
|-
|}

{{notelist|refs=
<ref name="301E">This is fullwidth version of {{unichar|2033}}. In vertical texts, {{unichar|301F}} is preferred.</ref>
<ref name="Vertical presentation forms">These characters are not used in typical documents. Instead the respective horizontal characters are used and the character that is rendered depends on the [[Horizontal_and_vertical_writing_in_East_Asian_scripts#In_computing|writing direction]].</ref>
<ref name="FE18">The original name of this character is "Presentation Form For Vertical Right White Lenticular {{sic|Brakcet}}". Since Unicode character names cannot be changed, this character has the corrected name as an [[Unicode_alias_names_and_abbreviations|alias]].</ref>
}}

==See also==
* [[Bracket (mathematics)]]
* [[International variation in quotation marks]]
* [[Emoticon]]
* [[Japanese typographic symbols]]
* [[Order of operations]]
* [[Triple parentheses]]

==References==
{{Reflist|30em|refs=
<ref name="Halfwidth and Fullwidth Forms">{{cite web |url= https://www.unicode.org/charts/PDF/UFF00.pdf |title=Halfwidth and Fullwidth Forms Code Chart |work=The Unicode Standard |publisher=Unicode Consortium |access-date=7 February 2016 |archive-date=22 February 2016 |archive-url= https://web.archive.org/web/20160222001703/https://www.unicode.org/charts/PDF/UFF00.pdf |url-status=live}}</ref>
<ref name="Basic Latin">{{cite web |url= https://www.unicode.org/charts/PDF/U0000.pdf |title=C0 Controls and Basic Latin Code Chart |work=The Unicode Standard |publisher=Unicode Consortium |access-date=27 February 2016 |archive-date=26 May 2016 |archive-url= https://web.archive.org/web/20160526182105/http://www.unicode.org/charts/PDF/U0000.pdf |url-status=live}}</ref>
<ref name="Unicode Superscripts and Subscripts">{{cite web |url= https://www.unicode.org/charts/PDF/U2070.pdf |title=Superscripts and Subscripts Code Chart |work=The Unicode Standard |publisher=Unicode Consortium |access-date=27 February 2016 |archive-date=13 April 2018 |archive-url= https://web.archive.org/web/20180413025550/http://www.unicode.org/charts/PDF/U2070.pdf |url-status=live}}</ref>
<ref name="Unicode Miscellaneous Mathematical Symbols-A">{{cite web |url= https://www.unicode.org/charts/PDF/U27C0.pdf |title=Miscellaneous Mathematical Symbols-A Code Chart |work=The Unicode Standard |publisher=Unicode Consortium |access-date=7 February 2016 |archive-date=13 April 2018 |archive-url= https://web.archive.org/web/20180413030824/http://www.unicode.org/charts/PDF/U27C0.pdf |url-status=live}}</ref>
<ref name="Unicode Miscellaneous Mathematical Symbols-B">{{cite web |url= https://www.unicode.org/charts/PDF/U2980.pdf |title=Miscellaneous Mathematical Symbols-B Code Chart |work=The Unicode Standard |publisher=Unicode Consortium |access-date=7 February 2016 |archive-date=12 November 2018 |archive-url= https://web.archive.org/web/20181112231107/https://www.unicode.org/charts/PDF/U2980.pdf |url-status=live}}</ref>
<ref name="CJK Symbols and Punctuation">{{cite web |url= https://www.unicode.org/charts/PDF/U3000.pdf |title=CJK Symbols and Punctuation Code Chart |work=The Unicode Standard |publisher=Unicode Consortium |access-date=7 February 2016 |archive-date=7 April 2009 |archive-url= https://web.archive.org/web/20090407061216/http://www.unicode.org/charts/PDF/U3000.pdf |url-status=live}}</ref>
<ref name="Unicode Dingbats">{{cite web |url= https://www.unicode.org/charts/PDF/U2700.pdf |title=Dingbats Code Chart |work=The Unicode Standard |publisher=Unicode Consortium |access-date=7 February 2016 |archive-date=17 April 2018 |archive-url= https://web.archive.org/web/20180417062019/http://unicode.org/charts/PDF/U2700.pdf |url-status=live}}</ref>
<ref name="Supplemental Punctuation">{{cite web |url= https://www.unicode.org/charts/PDF/U2E00.pdf |title=Supplemental Punctuation Code Chart |work=The Unicode Standard |publisher=Unicode Consortium |access-date=7 February 2016 |archive-date=24 November 2021 |archive-url= https://web.archive.org/web/20211124073722/https://www.unicode.org/charts/PDF/U2E00.pdf |url-status=live}}</ref>
<ref name="General Punctuation">{{cite web |url= https://www.unicode.org/charts/PDF/U2000.pdf |title=General Punctuation Code Chart |work=The Unicode Standard |publisher=Unicode Consortium |access-date=1 March 2016 |archive-date=3 March 2016 |archive-url= https://web.archive.org/web/20160303175510/http://www.unicode.org/charts/PDF/U2000.pdf |url-status=live}}</ref>
<ref name="Unicode Phonetic Punctuation">{{cite web |url= https://www.unicode.org/L2/L2021/21042-phonetic%20punct.pdf |title=L2/21-042: Unicode request for phonetic punctuation & diacritics |date=11 January 2021 |first=Kirk |last=Miller |access-date=19 November 2022 |archive-date=8 October 2022 |archive-url= https://web.archive.org/web/20221008021915/http://www.unicode.org/L2/L2021/21042-phonetic%20punct.pdf |url-status=live}}</ref>
<ref name="Unicode Arabic Presentation Forms">{{cite web |url= https://www.unicode.org/charts/PDF/UFB50.pdf |title=Arabic Presentation Forms-A Code Chart |work=The Unicode Standard |publisher=Unicode Consortium |access-date=7 February 2016 |archive-date=28 April 2014 |archive-url= https://web.archive.org/web/20140428184606/http://unicode.org/charts/PDF/UFB50.pdf |url-status=live}}</ref>
<ref name="Unicode Miscellaneous Technical">{{cite web |url= https://www.unicode.org/charts/PDF/U2300.pdf |title=Miscellaneous Technical Code Chart |work=The Unicode Standard |publisher=Unicode Consortium |access-date=7 February 2016 |archive-date=30 December 2019 |archive-url= https://web.archive.org/web/20191230040331/http://unicode.org/charts/PDF/U2300.pdf |url-status=live}}</ref>
<ref name="Small Form Variants">{{cite web |url= https://www.unicode.org/charts/PDF/U2300.pdf |title=Small Form Variants|work=The Unicode Standard |publisher=Unicode Consortium}}</ref>
<ref name="CJK Compatibility Forms">{{cite web |url= https://www.unicode.org/charts/PDF/UFE30.pdf|title=CJK Compatibility Forms|work=The Unicode Standard |publisher=Unicode Consortium}}</ref>
<ref name="Vertical Forms">{{cite web |url= https://www.unicode.org/charts/PDF/UFE10.pdf|title=Vertical Forms|work=The Unicode Standard |publisher=Unicode Consortium}}</ref>
}}
=== Sources ===
{{refbegin}}
* {{cite book|title=Concise Oxford Companion to the English Language|chapter=Brackets|author1-first=Thomas Burns|author1-last=McArthur|author1-link=Tom McArthur (linguist)|author2-first=Roshan|author2-last=McArthur|publisher=Oxford University Press|year=2005|isbn=9780192806376}}
* {{cite book|title=Words: A User's Guide|author1-first=Graham|author1-last=Pointon|author2-first=Stewart|author2-last=Clark|publisher=Routledge|year=2014|isbn=9781317864295|chapter=Punctuation Guide}}
* {{cite book|title=The Cambridge Guide to Australian English Usage|author1-first=Pam|author1-last=Peters|author1-link=Pam Peters|edition=2nd|publisher=Cambridge University Press|year=2007|isbn=9781139465212}}
* {{cite encyclopaedia|encyclopaedia=A Dictionary of Chemistry and the Allied Branches of Other Sciences|volume=4|author1-first=Henry|author1-last=Watts|author1-link=Henry Watts (chemist)|publisher=Longmans, Green, and Company|year=1877|article=Notation}}
* {{cite book|title=Learning the Bash Shell|author1-first=Cameron|author1-last=Newham|author2-first=Bill|author2-last=Rosenblatt|publisher=O'Reilly Media|year=1998|isbn=9781565923478}}
* {{cite book|title=A Practical Guide to UNIX for Mac OS X Users|author1-first=Mark G.|author1-last=Sobell|author2-first=Peter|author2-last=Seebach|publisher=Prentice Hall Professional|year=2005|isbn=9780321629982}}
* {{cite book|title=Discrete Mathematics|author1-first=Norman|author1-last=Biggs|publisher=OUP Oxford|year=2002|isbn=9780198507178|chapter=Set notation}}
* {{cite book|title=The Development of Modern Chemistry|series=Dover Books on Chemistry|author1-first=Aaron J.|author1-last=Ihde|publisher=Courier Corporation|year=1984|isbn=9780486642352}}
* {{cite book|title=Technical Shop Mathematics|author1-first=Thomas|author1-last=Achatz|author2-first=John G.|author2-last=Anderson|editor1-first=Kathleen|editor1-last=McKenzie|publisher=Industrial Press|year=2005|isbn=9780831130862}}
* {{cite book|title=Treatise on English Punctuation|author1-first=John|author1-last=Wilson|edition=2nd|location=Boston|year=1850}}
* {{cite book|title=An Essay on Punctuation|author1-first=Joseph|author1-last=Robertson|author1-link=Joseph Robertson (priest)|publisher=J. Walter|location=London|year=1785}}
* {{cite book|title=A Course of Mathematics|volume=1|edition=11th|author1-first=Charles|author1-last=Hutton|author1-link=Charles Hutton|editor1-first=Olinthus|editor1-last=Gregory|publisher=Longman, Rees|location=London|year=1836}}
{{refend}}

==Bibliography==
* {{cite book |author-link=John Lennard |last=Lennard |first=John |title=But I Digress: The Exploitation of Parentheses in English Printed Verse |date=1991 |isbn=0198112475 |publisher=Clarendon Press |location=Oxford}}
* {{cite book |last1=Turnbull |first1=Arthur T. |last2=Baird |first2=Russell N. |title=The Graphics of Communication: Typography, Layout, Design |publisher=Holt, Rinehart and Winston |location=New York |date=1964}} 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}}

{{navbox punctuation}}
[[Category:Punctuation]]
[[Category:Mathematical notation]]