Editing Bracket (section)

==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}}