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*LEFT [ANGLE BRACKET]* —>
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*RIGHT [ANGLE BRACKET]* —>
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The symbols ⟨ and ⟩ are angle brackets in both American and British English
In (largely archaic) computer slang, they were sometimes known as “brokets”
Strictly speaking they are distinct from V-shaped chevrons, as they have (where the typography permits it) a broader span than chevrons,[66] although when printed often no visual distinction is made
The ASCII less-than and greater-than characters < and > are often used for angle brackets. In many cases, only those characters are accepted by computer programs, and the Unicode angle brackets are not recognized (for instance, in HTML tags). The characters for “single” guillemets (‹ and ›) are also often used, and sometimes normal guillemets (« and ») when nested angle brackets are needed.
The angle brackets or chevrons U+27E8 ⟨ MATHEMATICAL LEFT ANGLE BRACKET and U+27E9 ⟩ MATHEMATICAL RIGHT ANGLE BRACKET are for mathematical use and Western languages, whereas U+3008 〈 LEFT ANGLE BRACKET and U+3009 〉 RIGHT ANGLE BRACKET are for East Asian languages. The chevrons at U+2329 and U+232A are deprecated in favour of the U+3008 and U+3009 East Asian angle brackets. Unicode discourages their use for mathematics and in Western texts,[14] 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.
⟨ and ⟩ were tied to the deprecated symbols U+2329 and U+232A in HTML4 and MathML2, but are being migrated to U+27E8 and U+27E9 for HTML5 and MathML3, as defined in XML Entity Definitions for Characters (Archived 27 January 2013 at the Wayback Machine).
Shape
Angle brackets are larger than less-than and greater-than signs, which in turn are larger than guillemets.
Angle brackets, less-than/greater-than signs and single guillemets in fonts Cambria, DejaVu Serif, Andron Mega Corpus, Andika and Everson Mono
Uses of ⟨ ⟩
Angle brackets are infrequently used to denote words that are thought instead of spoken, such as:
⟨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.[67]
In comic books, chevrons are often used to mark dialogue that has been translated notionally from another language; in other words, if a character is speaking another language, instead of writing in the other language and providing a translation, one writes the translated text within chevrons. Since no foreign language is actually written, this is only notionally translated.[citation needed]
In linguistics, angle brackets identify graphemes (e.g., letters of an alphabet) or orthography, as in “The English word /kæt/ is spelled ⟨cat⟩.”[68][69][67] (See IPA Brackets and transcription delimiters.)
In epigraphy, they may be used for mechanical transliterations of a text into the Latin script.[69]
In East Asian punctuation, angle brackets are used as quotation marks. Chevron-like symbols are part of standard Chinese, Japanese and – less frequently – Korean punctuation, where they generally enclose the titles of books, as: 〈 ︙ 〉 or 《 ︙ 》 for traditional vertical printing — written in vertical lines — and as 〈 … 〉 or 《 … 》 for horizontal printing — in horizontal.
Angle brackets in mathematics
Main article: Glossary of mathematical symbols § ⟨⟩
Angle brackets (or ‘chevrons’) are used in group theory to write group presentations, and to denote the subgroup generated by a collection of elements. In set theory, chevrons or parentheses are used to denote ordered pairs[70] and other tuples, 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) over time or over another continuous parameter. For example:
⟨
V
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t
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2
⟩
lim
T
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∞
1
T
∫
−
T
2
T
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V
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t
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{\displaystyle \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.}
In mathematical physics, especially quantum mechanics, it is common to write the inner product between elements as ⟨a|b⟩, as a short version of ⟨a|·|b⟩, or ⟨a|Ô|b⟩, where Ô is an operator. This is known as Dirac notation or bra–ket notation, to note vectors from the dual spaces of the Bra ⟨A| and the Ket |B⟩. But there are other notations used.
In continuum mechanics, chevrons may be used as Macaulay brackets.
Angle brackets in programming languages
Look up angle bracket, ⟨ ⟩, < >, broket, pointy bracket, or diamond bracket in Wiktionary, the free dictionary.
In C++ angle brackets (actually less-than and greater-than) are used to surround arguments to templates. They are also used to surround the names of header files; this usage was inherited from and is also found in C.
In the 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 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 . This use is sometimes extended as an informal mechanism for communicating mood or tone in digital formats such as messaging, for example adding “” at the end of a sentence.
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