“Bracket”的意思、由来-开放百科全书

A bracket is a tall punctuation mark commonly used in matched pairs within text, to set apart or interject other text. The matched pair is best described as opening and closing.^[1] Less formally, in a left-to-right context, it may be described as left and right, and in a right-to-left context, as right and left.

Forms include round (also called "parentheses"), square, curly (also called "braces"), and angle brackets (also called "chevrons"), as well as various other pairs of symbols.

In addition to referring to the class of all types of brackets, the unqualified word bracket is most commonly used to refer to a specific type of bracket; in modern American usage, this is usually the square bracket and in modern British usage, this is usually the round bracket.

History

Chevrons, ⟨ ⟩, were the earliest type of bracket to appear in written English. Desiderius Erasmus coined the term lunula to refer to the rounded parentheses, (), recalling the shape of the crescent moon.^[2]

Names for various bracket symbols

Typography

The characters ‹ › and « », known as {{lang|fr|guillemets}} or angular quote brackets, are actually quotation mark glyphs used in several European languages.^[7] Which one of each pair is the opening quote mark and which is the closing quote varies between languages.

Similarly, the corner-brackets ｢｣ are quotation marks used in East Asian languages (see Quotation mark § Chinese, Japanese and Korean quotation marks).

In English, typographers mostly prefer not to set brackets in italics, even when the enclosed text is italic.^[8] However, in other languages like German, if brackets enclose text in italics, they are usually also set in italics.^[9]

Types and uses

Parentheses {{Anchor|Parenthesis}}

Usage in writing

Parentheses {{IPAc-en|p|ə|ˈ|r|ɛ|n|θ|ᵻ|s|iː|z}} (singular, parenthesis {{IPAc-en|p|ə|ˈ|r|ɛ|n|θ|ᵻ|s|ᵻ|s}}) (also called simply brackets, or round brackets, curves, curved brackets, oval brackets, stalls or, colloquially, parens {{IPAc-en|p|ə|ˈ|r|ɛ|n|z}}) contain material that serves to clarify (in the manner of a gloss) or is aside from the main point.^[10] A milder effect may be obtained by using a pair of commas as the delimiter, though if the sentence contains commas for other purposes, visual confusion may result.

In American usage, parentheses are usually considered separate from other brackets, and calling them "brackets" is unusual.

Parentheses may be used in formal writing to add supplementary information, such as "Sen. John McCain (R-Arizona) spoke at length". They can also indicate shorthand for "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".^[11]

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 Quentin section of The Sound and the Fury) as well as poet E. E. Cummings.

Parentheses have historically been used where the dash is currently used in alternatives, such as "parenthesis)(parentheses". Examples of this usage can be seen in editions of Fowler's.

Parentheses may be nested (generally with one set (such as this) inside another set). Thus secondary, or even tertiary, phrases can be found within the main parenthetical sentence.

Any punctuation inside parentheses or other brackets is independent of the rest of the text: "Mrs. Pennyfarthing (What? Yes, that was her name!) was my landlady." In this usage, the explanatory text in the parentheses is a parenthesis. Parenthesized text is usually short and within a single sentence. Where several sentences of supplemental material are used in parentheses the final full stop would be within the parentheses, or simply omitted. Again, the parenthesis implies that the meaning and flow of the text is supplemental to the rest of the text and the whole would be unchanged were the parenthesized sentences removed.

In more formal usage, "parenthesis" may refer to the entire bracketed text, not just to the punctuation marks used (so all the text in this set of round brackets may be said to be "a parenthesis", "a parenthetical", or "a parenthetical phrase").^[12]

Usage in enumerations

Unpaired parenthesis

Lower-case Latin letters used as indexes, rather than bullets or numbers, followed by an unpaired parenthesis, are used in ordered lists especially in:

Usage in mathematics

Parentheses are used in mathematical notation to indicate grouping, often inducing a different order of operations. For example: in the usual order of algebraic operations, {{math|4 x 3 + 2}} equals 14, since the multiplication is done before the addition. However, {{math|4 x (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:

A related convention is that when parentheses have two levels of nesting, curly brackets (braces) are the outermost pair. Following this convention, when more than three levels of nesting are needed, often a cycle of parentheses, square brackets, and curly brackets will continue. This helps to distinguish between one such level and the next.^[13]

Parentheses are also used to set apart the arguments in mathematical functions. For example, {{math|f(x)}} is the function {{math|f}} applied to the variable {{math|x}}. In coordinate systems parentheses are used to denote a set of coordinates; so in the Cartesian coordinate system {{math|(4, 7)}} may represent the point located at 4 on the x-axis and 7 on the y-axis.

Usage in programming languages

Parentheses are included in the syntaxes of many programming languages. Typically needed to denote an argument; to tell the compiler what data type the Method/Function needs to look for first in order to initialise. In some cases, such as in LISP, parentheses are a fundamental construct of the language. They are also often used for scoping functions and for arrays.

Usage in other scientific fields

Parentheses are used in chemistry to denote a repeated substructure within a molecule, e.g. HC(CH₃)₃ (isobutane) or, similarly, to indicate the stoichiometry of ionic compounds with such substructures: e.g. Ca(NO₃)₂ (calcium nitrate).

They can be used in various fields as notation to indicate the amount of uncertainty in a numerical quantity. For example:^[14]

eg the value of the Boltzmann constant could be quoted as {{val|1.38064852|(79)|e=-23}} J⋅K⁻¹

Usage online

Many online Roleplayers use double parentheses to connotate out-of-character (OOC) messages that one may send another.

Square brackets {{Anchor|square bracket}}

Usage in published text

Square brackets—also called crotchets or simply brackets (US)—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.^[15]

A bracketed ellipsis, […], is often used to indicate omitted material: "I'd like to thank [several unimportant people] for their tolerance [...]"^[16]

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 text is omitted for succinctness, for example, when referring to a verbose original: "To the extent that policymakers and elite opinion in general have made use of economic analysis at all, they have, as the saying goes, done so the way a drunkard uses a lamppost: for support, not illumination", it can be quoted succinctly as: "[P]olicymakers […] made use of economic analysis […] the way a drunkard uses a lamppost: for support, not illumination." When nested parentheses are needed, brackets are used as a substitute for the inner pair of parentheses within the outer pair.^[17] When deeper levels of nesting are needed, convention is to alternate between parentheses and brackets at each level.

Alternatively, empty square brackets can also indicate omitted material, usually single letter only. The original "Reading is also a process and it also changes you." can be rewritten in a quote as: It has been suggested that reading can "also change[] you".

The bracketed expression "[sic]" is used after a quote or reprinted text to indicate the passage appears exactly as in the original source, where it may otherwise appear that a mistake has been made in reproduction.

In translated works, brackets are used to signify the same word or phrase in the original language to avoid ambiguity.^[18]

Usage in proofreading

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

Usage in scientific fields

Brackets are used in mathematics in a variety of notations, including standard notations for commutators, the floor function, the Lie bracket, equivalence classes, the Iverson bracket, and matrices. Square brackets may also represent closed intervals;

for example, represents the set of real numbers from 0 to 5 inclusive.

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 ion), repeating chemical units (particularly in polymers) and transition state structures, among other uses.

Brackets are used in many computer programming languages, primarily to force the order of evaluation and for parameter lists and array indexing. But they are also used to denote general tuples, sets and other structures, just as in mathematics. There may be several other uses as well, depending on the language at hand.

Other uses

In linguistics, phonetic transcriptions are generally enclosed within brackets,^[19] often using the International Phonetic Alphabet, whereas phonemic transcriptions typically use paired slashes. Pipes (| |) are often used to indicate a morphophonemic rather than phonemic representation. Other conventions are double slashes (// //), double pipes (|| ||) and curly brackets ({ }). In lexicography, square brackets usually surround the section of a dictionary entry which contains the etymology of the word the entry defines.

Brackets are used to denote parts of the text that need to be checked when preparing drafts prior to finalizing a document. They often denote points that have not yet been agreed to in legal drafts and the year in which a report was made for certain case law decisions.

Curly brackets {{anchor|Braces|Curly bracket}}

Curly brackets { and } are also known as curly braces (UK and US), flower brackets(India) and squiggly brackets(colloquially). They are rarely used in prose and have no widely accepted use in formal writing, but may be used to mark words or sentences that should be taken as a group, to avoid confusion when other types of brackets are already in use, or for a special purpose specific to the publication (such as in a dictionary).^[20] More commonly, they are used to indicate a group of lines that should be taken together, as in when referring to several lines of poetry that should be repeated.

In music, they are known as accolades or "braces", and connect two or more lines (staves) of music that are played simultaneously.^[21]

In mathematics they delimit sets, and in writing, they may be used similarly, "Select your animal {goat, sheep, cow, horse} and follow me". In many programming languages, they enclose groups of statements and create a local scope. Such languages (C being one of the best-known examples) are therefore called curly bracket languages.^[22] In classical mechanics, curly brackets are often also used to denote the Poisson bracket between two quantities.

Angle brackets {{anchor|Chevrons}}

Chevrons {{angbr| }}, similar to the commonly used less-than (<) and greater-than sign (>), are often used to enclose highlighted material.

In physical sciences, chevrons are used to denote an average over time or over another continuous parameter. For example,

The inner product of two vectors is commonly written as {{math|{{angbr|a,b}}}}, but there are other notations used.

In mathematical physics, especially quantum mechanics, it is common to write the inner product between elements as {{math|{{bra-ket|a|b}}}}, as a short version of {{math|{{bra|a}}·{{ket|b}}}}, or {{math|{{bra|a}}Ô{{ket|b}}}}, where {{math|Ô}} is an operator. This is known as Dirac notation or bra–ket notation.

In set theory, chevrons or parentheses are used to denote ordered pairs and other tuples, whereas curly brackets are used for unordered sets.

In linguistics, chevrons indicate graphemes (i.e., written letters) or orthography, as in "The English word {{IPA|/kæt/}} is spelled {{angbr|cat}}."^[23]^[24]^[25]

In epigraphy, they may be used for mechanical transliterations of a text into the Latin script.^[24]

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.^[25]

In HTML, chevrons (greater and less than symbols) are used to bracket meta text. For example “<b>” 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 “</b>”. This usage is sometimes extended as a mechanism for communicating mood, or tone, in digital formats such as messaging, for example adding “<sighs>” at the end of a sentence.

Chevrons are infrequently used to denote words that are thought instead of spoken, such as:

The mathematical or logical symbols for greater-than (>) and less-than (<) are inequality symbols; when either symbol is bisected by a vertical line, it represents "not greater than" or "not less than," respectively. These symbols are not punctuation marks when used, as intended, to represent an inequality. However, as true chevrons are not present on computer keyboards, the available less-than and greater-than symbols are often used instead. They are loosely referred to as angle[d] brackets or chevrons in this case, but more properly—and less confusingly—as pointy brackets (see the Names section above).{{citation needed|date=November 2012}}

Single and double pairs of comparison operators (<<, >>) (meaning much smaller than and much greater than) are sometimes used as a fallback instead of guillemets («, ») (used as quotation marks in many languages) when the proper characters are not available on the keyboard nor in the input editor. Similarly, early Internet messaging conventions developed to use the greater-than sign (>), available in the ASCII character set, to mark quoted lines. This format, known as Usenet quoting, is used by email clients when operating in plain text mode.

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

In East Asian punctuation, angle brackets are used as quotation marks. Chevron-like symbols are part of standard Chinese, and Korean punctuation, where they generally enclose the titles of books: ︿ and ﹀ or ︽ and ︾ for traditional vertical printing, and 〈 and 〉 or 《 and 》 for horizontal printing.

Lenticular brackets

Some East Asian languages use lenticular brackets 【】, a combination of square brackets and round brackets called {{lang|zh|方頭括號}} (fāngtóu kuòhào) in Chinese and {{lang|ja|

すみ付き}} (sumitsuki) in Japanese. {{clarify|text=They are used for inference in Chinese|date=April 2017}} and used in titles and headings in Japanese.

Floor and ceiling corners

The floor corner brackets ⌊ and ⌋, the ceiling corner brackets ⌈ and ⌉ are used to denote the integer floor and ceiling functions.

Quine corners and half brackets

The Quine corners ⌜ and ⌝ have at least two uses in mathematical logic: either as quasi-quotation, a generalization of quotation marks, or to denote the Gödel number of the enclosed expression.

Half brackets are used in English to mark added text, such as in translations: "Bill saw ⸤her⸥".

In editions of 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.^[26] 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.^[29]

Double brackets

Double brackets (or white square brackets), ⟦ ⟧, are used to indicate the semantic evaluation function in formal semantics for natural language and denotational semantics for programming languages.^[27]^[28] The brackets stand for a function that maps a linguistic expression to its “denotation” or semantic value. Double brackets may also refer to the mathematical floor function.

Brackets with quills

Known as "spike parentheses" ({{lang-sv|piggparenteser}}) ⁅ and ⁆ are used in Swedish dictionaries.^[29]

Specific uses

Computing

The various bracket characters are frequently used in many programming languages as operators or for other syntax markup. For instance, in C-like languages, { and } are often used to delimit a code block, and the parameters of method calls are generally enclosed by ( and ).

In C, C++, Java and other C-derived languages—as well as in Scheme-influenced languages that have adopted C/Java syntax, such as JavaScript—the "{}" symbols are referred to as "braces" or "curly braces" and never as brackets. Since the term "brace" is documented in the definitive programming specifications for these languages, it is preferable to use the correct term brace so there is no confusion between the brace (used to denote compound statements) and the bracket, used to denote other concepts, such as array indices.^[30]^[31]

Mathematics

In addition to the use of parentheses to specify the order of operations, both parentheses and brackets are used to denote an interval, also referred to as a half-open range. The notation {{closed-open|{{mvar|a}},{{mvar|c}}}} is used to indicate an interval from {{mvar|a}} to {{mvar|c}} that is inclusive of {{mvar|a}} but exclusive of {{mvar|c}}. That is, {{closed-open|5, 12}} would be the set of all real numbers between 5 and 12, including 5 but not 12. The numbers may come as close as they like to 12, including 11.999 and so forth (with any finite number of 9s), but 12.0 is not included. In some European countries, the notation {{math|[5, 12[}} is also used for this. The endpoint adjoining the bracket is known as closed, whereas the endpoint adjoining the parenthesis is known as open. If both types of brackets are the same, the entire interval may be referred to as closed or open as appropriate. Whenever +∞ or −∞ is used as an endpoint, it is normally considered open and adjoined to a parenthesis. See Interval (mathematics) for a more complete treatment.

In quantum mechanics, chevrons are also used as part of Dirac's formalism, bra–ket notation, to note vectors from the dual spaces of the Bra {{angbr|{{math|A|}} and the Ket {{math||B}}}}. Mathematicians will also commonly write {{angbr|{{math|a, b}}}} for the inner product of two vectors. In statistical mechanics, chevrons denote ensemble or time average. Chevrons are used in group theory to write group presentations, and to denote the subgroup generated by a collection of elements. Note that obtuse angled chevrons are not always (and even not by all users) distinguished from a pair of less-than and greater-than signs <>, which are sometimes used as a typographic approximation of chevrons.

In group theory and ring theory, brackets denote the commutator. In group theory, the commutator {{math|[{{mvar|g}}, {{mvar|h}}]}} is commonly defined as {{math|{{mvar|g}}⁻¹ {{mvar|h}}⁻¹ {{mvar|g}} {{mvar|h}} }}. In ring theory, the commutator {{math|[{{mvar|a}}, {{mvar|b}}]}} is defined as {{math|{{mvar|a}} {{mvar|b}} − {{mvar|b}} {{mvar|a}} }}. Furthermore, in ring theory, braces denote the anticommutator where {{math|{{{mvar|a}}, {{mvar|b}}}}} is defined as {{math|{{mvar|a}} {{mvar|b}} + {{mvar|b}} {{mvar|a}} }}. The bracket is also used to denote the Lie derivative, or more generally the Lie bracket in any Lie algebra.

Various notations, like the vinculum have a similar effect to brackets in specifying order of operations, or otherwise grouping several characters together for a common purpose.

In the Z formal specification language, braces define a set and chevrons define a sequence.

Accounting

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

Citations

When quoted material is in any way altered, the alterations are enclosed in square brackets within the quotation. For example: Plaintiff asserts his cause is just, stating, "[m]y causes is {{bracket|sic}} just." Although in the original quoted sentence the word "my" was capitalized, it has been modified in the quotation and the change signalled with brackets. Similarly, where the quotation contained a grammatical error, the quoting author signalled that the error was in the original with "[sic]" (Latin for 'thus'). (California Style Manual, section 4:59 (4th ed.))

Law

Square brackets are used in some countries in the citation of law reports to identify parallel citations to non-official reporters. For example: Chronicle Pub. Co. v. Superior Court, (1998) 54 Cal.2d 548, [7 Cal.Rptr. 109]. In some other countries (such as England and Wales), square brackets are used to indicate that the year is part of the citation and parentheses are used to indicate the year the judgment was given. For example, National Coal Board v England [1954] AC 403, is in the 1954 volume of the Appeal Cases reports although the decision may have been given in 1953 or earlier, whereas (1954) 98 Sol Jo 176 reports a decision from 1954, in volume 98 of the Solicitor's Journal which may be published in 1955 or later.

Sports

Tournament brackets, the diagrammatic representation of the series of games played during a tournament usually leading to a single winner, are so named for their resemblance to brackets or braces.

{{anchor|Encoding}}Encoding in digital media

Representations of various kinds of brackets in Unicode and HTML are given below.

1. ^UAX #9: Unicode Bidirectional Algorithm, {{cite web|url=https://www.unicode.org/reports/tr9/#Paired_Brackets |title=3.1.3 Paired Brackets |access-date=24 April 2018 |website=unicode.org}}
2. ^Truss, Lynne. Eats, Shoots & Leaves, 2003. p. 161. {{ISBN|1-59240-087-6}}.
3. ^Concise Oxford Dictionary, 10th Edition, Oxford University Press, Great Clarendon Street, Oxford OX2 2DP, UK
4. ^Smith, John. The Printer’s Grammar p. 84.
5. ^{{cite web|url=http://catb.org/jargon/html/B/broket.html |title=broket |publisher=Catb.org |date= |accessdate=2013-02-13}}
6. ^{{cite web |url=https://www.microsoft.com/language/en-us/Search.aspx?sString=chevron&langID=de-de |title=Terminology Search - Microsoft |website=Microsoft Language Portal - Terminology Collection|date= |author= |accessdate= 21 November 2016}}
7. ^{{cite book|title=Merriam-Webster's Manual for Writers and Editors|year=1998|publisher=Merriam-Webster|page=149|url=https://books.google.com/books?id=7C6V9zRxSPkC&pg=PA149&|isbn=0-87779-622-X |via=Google Books}}
8. ^Robert Bringhurst, The Elements of Typographic Style, §5.3.2.
9. ^{{cite book |last1=Forsmann |first1=Friedrich |last2=DeJong |first2=Ralf |date=2004 |title=Detailtypografie |trans-title=Detail Typography |language=German |location=Mainz |publisher= Herrmann Schmidt |page=263 |isbn= 978-3874396424}}
10. ^{{cite web|last=Straus|first=Jane|author-link=Jane Straus|title=Parentheses—Punctuation Rules|url=http://www.grammarbook.com/punctuation/parens.asp|work=The Blue Book of Grammar and Punctuation|publisher=grammarbook.com|accessdate=18 April 2014}}
11. ^Slash (punctuation)#Gender-neutrality in Spanish and Portuguese
12. ^{{cite web|url=http://www.thefreedictionary.com/parenthetical |title=The Free Online Dictionary |publisher=Thefreedictionary.com |date= |accessdate=2013-02-13}}
13. ^{{cite web|url=http://math.about.com/od/mathhelpandtutorials/fl/Parenthesis-Braces-and-Brackets.html |title=Archived copy |accessdate=2014-08-01 |deadurl=yes |archiveurl=https://archive.is/20140806203819/http://math.about.com/od/mathhelpandtutorials/fl/Parenthesis-Braces-and-Brackets.html |archivedate=6 August 2014 }}
14. ^{{cite web | url=http://physics.nist.gov/cgi-bin/cuu/Info/Constants/definitions.html | title=Standard Uncertainty and Relative Standard Uncertainty | work=CODATA reference | publisher=NIST | accessdate=2018-07-20 }}
15. ^The Chicago Manual of Style, 15th ed., The University of Chicago Press, 2003, §6.104
16. ^{{cite web|url=http://www.bartleby.com/68/60/960.html |title=Bartleby.com: Great Books Online -- Quotes, Poems, Novels, Classics and hundreds more |work=bartleby.com |deadurl=yes |archiveurl=https://web.archive.org/web/20080524214802/http://www.bartleby.com/68/60/960.html |archivedate=24 May 2008 |df=dmy }}
17. ^The Chicago Manual of Style, 15th ed., The University of Chicago Press, 2003, §6.102 and §6.106
18. ^The Chicago Manual of Style, 15th ed., The University of Chicago Press, 2003, §6.105
19. ^The Chicago Manual of Style, 15th ed., The University of Chicago Press, 2003, §6.107
20. ^{{cite web|url=https://english.stackexchange.com/questions/127892/are-curly-braces-ever-used-in-normal-text-if-not-why-were-they-created |title=Are curly braces ever used in normal text? If not, why were they created? |access-date=24 April 2018 |website=Stack Exchange}}
21. ^{{cite web|url=http://www.decodeunicode.org/u%2B007B |title=> U+007B LEFT CURLY BRACKET |website= Decodeunicode.org {{^|access-date=3 May 2009}} |dead-url=yes |archive-url= https://web.archive.org/web/20081202121802/http://www.decodeunicode.org/u%2B007B |archive-date=2 December 2008}}
22. ^{{cite web|url=http://www.riedquat.de/prog/style |title=Brace and Indent Styles and Code Convention |work=riedquat.de |deadurl=yes |archiveurl=https://web.archive.org/web/20150924070732/http://www.riedquat.de/prog/style |archivedate=24 September 2015 |df= }}
23. ^{{cite book|last1=Bauer|first1=Laurie|title=The Linguistics Student's Handbook|date=2007|publisher=Edinburgh University Press|location=Edinburgh|page=99|chapter-url=https://books.google.com/books?id=WsrtrmHkLvoC&pg=PA99|chapter=Notational conventions. Brackets}}
24. ^¹{{cite book|last1=Sampson|first1=Geoffrey|editor1-last=Allan|editor1-first=Keith|title=The Routledge Handbook of Linguistics|date=2016|publisher=Routledge|page=60|chapter-url=https://books.google.com/books?id=3vssCgAAQBAJ&pg=PA60|chapter=Writing systems: methods for recording language}}
25. ^¹{{cite book|last1=Trask|first1=Robert Lawrence|title=The Dictionary of Historical and Comparative Linguistics|date=2000|publisher=Edinburgh University Press|location=Edinburgh|page=22|chapter-url=https://books.google.com/books?id=EHeGzQ8wuLQC&pg=PA22|chapter=Angle brackets}}
26. ^M.L. West (1973) Textual Criticism and Editorial Technique (Stuttgart) 81.
27. ^Dowty, D., Wall, R. and Peters, S.: 1981, Introduction to Montague semantics, Springer.
28. ^Scott, D. and Strachey, C.: 1971, Toward a mathematical semantics for computer languages, OxfordUniversity Computing Laboratory, Programming Research Group.
29. ^See sv:Parentes
30. ^Brian W. Kernighan, Dennis M. Ritchie. "The C Programming Language", 1988. p. 7. {{ISBN|0-13-110370-9}}
31. ^Bjarne Stroustrup, "The C++ Programming Language", 2013. p.39. {{ISBN|0-13-352285-7}}
32. ^¹{{citation | url=https://www.unicode.org/charts/PDF/U0000.pdf | title=C0 Controls and Basic Latin Code Chart | work=The Unicode Standard | accessdate=2016-02-27}}
33. ^{{citation | url=https://www.unicode.org/charts/PDF/U0080.pdf | title=C1 Controls and Latin-1 Supplement Code Chart | work=The Unicode Standard | accessdate=2016-02-27}}
34. ^¹²³⁴⁵{{citation | url=https://www.unicode.org/charts/PDF/U2300.pdf | title=Miscellaneous Technical Code Chart | work=The Unicode Standard | accessdate=2016-02-27}}
35. ^{{citation | url=https://www.unicode.org/charts/PDF/U2070.pdf|title=Superscripts and Subscripts Code Chart|work=The Unicode Standard|accessdate=2016-02-27}}
36. ^{{citation | url=https://www.unicode.org/charts/PDF/U27C0.pdf | title=Miscellaneous Mathematical Symbols-A Code Chart | work=The Unicode Standard | accessdate=2016-02-27}}
37. ^{{citation | url=https://www.unicode.org/charts/PDF/U2980.pdf | title=Miscellaneous Mathematical Symbols-B Code Chart | work=The Unicode Standard | accessdate=2016-02-27}}
38. ^¹²³{{citation | url=https://www.unicode.org/charts/PDF/U2E00.pdf | title=Supplemental Punctuation Code Chart | work=The Unicode Standard | accessdate=2016-02-27}}
39. ^{{citation | url=https://www.unicode.org/charts/PDF/U2700.pdf | title=Dingbats Code Chart | work=The Unicode Standard | accessdate=2016-02-27}}
40. ^{{citation | url=https://www.unicode.org/charts/PDF/UFB50.pdf | title=Arabic Presentation Forms-A Code Chart | work=The Unicode Standard | accessdate=2016-02-27}}
41. ^{{citation | url=https://www.unicode.org/charts/PDF/U1680.pdf | title=Ogham Code Chart | work=The Unicode Standard | accessdate=2016-02-27}}
42. ^{{citation | url=https://www.unicode.org/charts/PDF/U0F00.pdf | title=Tibetan Code Chart | work=The Unicode Standard | accessdate=2016-02-27}}
43. ^¹{{citation | url=https://www.unicode.org/charts/PDF/U2000.pdf | title=General Punctuation Code Chart | work=The Unicode Standard | accessdate=2016-03-01}}
44. ^¹{{citation | url=https://www.unicode.org/charts/PDF/U3000.pdf | title=CJK Symbols and Punctuation Code Chart | work=The Unicode Standard | accessdate=2016-02-27}}
45. ^¹²{{citation | url=https://www.unicode.org/charts/PDF/UFF00.pdf | title=Halfwidth and Fullwidth Forms Code Chart | work=The Unicode Standard | accessdate=2016-02-27}}
46. ^&lang; and &rang; were tied to the deprecated symbols U+2329 and U+232A in HTML4 and MathML2, but are being migrated to U+27E8 and U+27E9 for HTML5 and MathML3, as defined in XML Entity Definitions for Characters.
47. ^This is fullwidth version of U+2033 DOUBLE PRIME. In vertical texts, U+301F LOW DOUBLE PRIME QUOTATION MARK is preferred.
48. ^{{cite web |last=Bob |first=Bemer |title=The Great Curly Brace Trace Chase |url=http://www.bobbemer.com/BRACES.HTM |accessdate =2009-09-05 |postscript=}}

Braces (curly brackets) first became part of a character set with the 8-bit code of the IBM 7030 Stretch.^[48]

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,^[34] 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.