Editing Bracket (section)

==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>
}}

The symbols {{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 (largely archaic) [[computer slang]], they were sometimes 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 {{char|<}} and {{char|>}} are often used for angle brackets. In many cases, only those characters are accepted by computer programs, and the Unicode angle brackets are not recognized (for instance, in [[HTML tag]]s). The characters for "single" [[guillemet]]s ({{char|‹}} and {{char|›}}) are also often used, and sometimes normal guillemets ({{char|«}} and {{char|»}}) when nested angle brackets are needed.

The angle brackets or chevrons {{unichar|27E8}} and {{unichar|27E9}} are for mathematical use and Western languages, whereas {{unichar|3008}} and {{unichar|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+300n 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]]]]
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===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" /> {{crossreference|(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====
{{Wiktionary pipe|angle bracket||⟨&nbsp;⟩||Unsupported titles/Enclosing less than greater than|<&nbsp;>|broket||pointy bracket||diamond bracket|}}
In [[C++]] angle brackets (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, angle brackets define a sequence.

In [[HTML]], angle brackets (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.

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