Bracket

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. Typically deployed in symmetric pairs, an individual bracket may be identified as a left or right bracket or, alternatively, an opening paired bracket or closing paired bracket,[1] respectively, depending on the directionality of the context.

This article is about the family of punctuation marks. For other uses, see Bracket (disambiguation).

"Parenthesis" and "parenthetical" redirect here. For other uses, see Parenthesis (disambiguation).

Brackets
( ) { } [ ] ⟨ ⟩ Round brackets Curly brackets Square brackets Angle brackets

Specific forms of the mark include rounded brackets (also called parentheses), square brackets, curly brackets (also called braces), and angle brackets (also called chevrons), as well as various less common pairs of symbols.

As well as signifying the overall class of punctuation, the word bracket is commonly used to refer to a specific form of bracket, which varies from region to region. In the United States, an unqualified 'bracket' typically refers to the square bracket; in Britain and most other English-speaking countries, 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 (Latin: luna).[2]

Names for various bracket symbols

Some of the following names are regional or contextual.

• ( ) – parentheses, brackets (UK, Ireland, Canada, West Indies, New Zealand, South Africa and Australia), parens, round brackets, first brackets, circle brackets or smooth brackets.
• { } – braces[3] (UK and US), curly brackets, definite brackets, swirly brackets, curly braces, birdie brackets, French brackets, Scottish brackets, squirrelly brackets, gullwings, seagulls, squiggly brackets, twirly brackets, Tuborg brackets (DK), accolades (NL), pointy brackets, second brackets, fancy brackets, M Brace, moustache brackets.
• [ ] – brackets (US), square brackets, closed brackets, hard brackets, third brackets, crotchets.[4]
• ⟨ ⟩ – angle brackets, less-than/greater-than signs (when the ASCII approximation of < > is used), pointy brackets, triangular brackets, diamond brackets, tuples, chevrons, guillemets, broken brackets, brokets.[5]
• ⸤ ⸥ ｢ ｣ – corner brackets
• ⟦ ⟧ – double square brackets, white square brackets, Scott brackets
• 〔 〕 – tortoise shell brackets

The characters ‹ › and « », known as guillemets or angle quotes, are actually quotation marks used in several European languages.[6] 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, though they have been repurposed for other contexts (see below).

Typography

In English, typographers mostly prefer not to set brackets in italics, even when the enclosed text is italic.[7] However, in other languages like German, if brackets enclose text in italics, they are usually also set in italics.[8]

Types and uses

Parentheses

Various terms redirect here. For other uses, see parenthesis (disambiguation), paren (disambiguation), parenthetical referencing, Parens (moth), ( ) (disambiguation), and Parenthetical Girls.

Due to technical restrictions, titles like :) redirect here. For typographical portrayals of faces, see emoticon.

Usage in writing

Parentheses /pəˈrɛnθɪsiːz/ (singular, parenthesis /pəˈrɛnθɪsɪs/) (also called simply brackets, or round brackets, curves, curved brackets, oval brackets, stalls or, colloquially, parens /pəˈrɛnz/) contain material that serves to clarify (in the manner of a gloss) or is aside from the main point.[9] 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. That issue is fixed by using a pair of dashes instead, to bracket the parenthetical.

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" (the slash in the second instance, as one alternative is replacing the other, not adding to it).[10]

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). 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]).

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").[11]

Usage in enumerations

Lower-case Latin letters used as indexes, rather than bullets or numbers, followed by an unpaired parenthesis, are used in ordered lists especially in:
a) educational testing,
b) technical writing and diagrams,
c) market research, and
d) elections.

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, 4 × 3 + 2 equals 14, since the multiplication is done before the addition. However, 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:

${\displaystyle [4\times (3+2)]^{2}=400.}$

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.[12]

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

Parentheses may be used to represent a binomial coefficient, and also matrices.

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. In syntax diagrams they are used for grouping eg in Extended Backus–Naur form.

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:[13]

1234.56789(11)

is equivalent to:

1234.56789 ± 0.00011

e.g. the value of the Boltzmann constant could be quoted as 1.38064852(79)×10⁻²³ J⋅K⁻¹

Square brackets

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.[14]

A bracketed ellipsis, [...], is often used to indicate omitted material: "I'd like to thank [several unimportant people] for their tolerance [...]"[15] 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 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.[16] 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.[17] For example: He is trained in the way of the open hand [karate].

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:

Move left	[To Fate I sue, of other means bereft, the only refuge for the wretched left.
Center	]Paradise Lost[
Move up

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; ${\displaystyle [0,5]}$ 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.

Usage in programming languages

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. In syntax diagrams they are used for optional eg in Extended Backus–Naur form.

Other uses

See also: International Phonetic Alphabet § Brackets and transcription delimiters

In linguistics, phonetic transcriptions are generally enclosed within square brackets,[18] 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.

Square 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

An example of curly brackets used to group sentences together

Curly brackets { and }, also known as curly braces (UK and US) or simply braces, flower brackets (India) and squiggly brackets (colloquially), 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).[19] 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.[20]

In mathematics they delimit sets, and in writing, they may be used similarly, "Select your animal {goat, sheep, cow, horse} and follow me". Curly brackets are often also used to denote the Poisson bracket between two quantities.

Usage in programming languages

In many programming languages, they enclose groups of statements and create a local scope. Such languages (C, C#, C++ and many others) are therefore called curly bracket languages.[21] They are used for enumerated type, eg in C. In syntax diagrams they are used for repetition eg in Extended Backus–Naur form.

Phonetics

As an extension to the International Phonetic Alphabet, braces are used for prosodic notation.

Angle brackets

"Angle bracket" redirects here. For a mechanical part used for joining, see Angle bracket (fastener).

Angle brackets ⟨ ⟩ (often substituted informally by less-than < and greater-than signs > or by "single" guillemets ‹ ›) are often used to enclose highlighted material.

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

${\displaystyle \left\langle V(t)^{2}\right\rangle =\lim _{T\to \infty }{\frac {1}{T}}\int _{-{\frac {T}{2}}}^{\frac {T}{2}}V(t)^{2}\,{\rm {d}}t.}$

The inner product of two vectors is commonly written as ⟨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 ⟨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.

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, angle brackets identify graphemes (i.e., letters of an alphabet) or orthography, as in "The English word /kæt/ is spelled ⟨cat⟩."[22][23][24]

In epigraphy, they may be used for mechanical transliterations of a text into the Latin script.[23]

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.[24]

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:

⟨ What an unusual flower! ⟩

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).

Single and double pairs of comparison operators <<, >> (meaning much smaller than and much greater than, although the single symbols ≪ and ≫ should be used for that purpose) 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. Since no foreign language is actually written, this is only notionally translated.

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

In East Asian punctuation, angle brackets are used as quotation marks. Chevron-like symbols are part of standard Chinese, Japanese 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 方頭括號 (fāngtóu kuòhào) in Chinese and すみ付き (sumitsuki) in Japanese. They are used for inference in Chinese and used in titles and headings in Japanese.

Floor and ceiling corners

The floor corner brackets ⌊ and ⌋, the ceiling corner brackets ⌈ and ⌉ (U+2308, U+2309) 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.[25] 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.[26]

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. In mathematics, double brackets may also be used to denote intervals of integers or, less often, the floor function. In papyrology, following the Leiden Conventions, they are used to enclose text that has been deleted in antiquity.[29]

Brackets with quills

Known as "spike parentheses" (Swedish: piggparenteser), ⁅ and ⁆, are used in Swedish bilingual dictionaries to enclose supplemental constructions.[30]

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.[31][32]

Mathematics

Main article: Bracket (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 [a,c) is used to indicate an interval from a to c that is inclusive of a but exclusive of c. That is, [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 [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 ⟨A| and the Ket |B⟩. Mathematicians will also commonly write ⟨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 [g, h] is commonly defined as g⁻¹ h⁻¹ g h . In ring theory, the commutator [a, b] is defined as a b − b a . Furthermore, in ring theory, braces denote the anticommutator where {a, b} is defined as a b + b 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 to show that the quotation is not exactly as given, or to add an annotation.[33] For example: The Plaintiff asserted his cause is just, stating,

[m]y causes is [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').

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.

Encoding in digital media

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

Usage	Unicode		SGML/HTML/XML entities	Sample
General purpose[34]	U+0028	Left parenthesis	( &lparen;	(parentheses)
	U+0029	Right parenthesis	) &rparen;
	U+005B	Left square bracket	[	[sic]
	U+005D	Right square bracket	]
Technical/mathematical (common)[34]	U+003C	Less-than sign	&#60; &lt;	<HTML>
	U+003E	Greater-than sign	&#62; &gt;
	U+007B	Left curly bracket	&#123;	{round, square, curly}
	U+007D	Right curly bracket	&#125;
Quotation (Western texts)[35][36]	U+00AB	Left-pointing double angle quotation mark	&#171;	« French quote » or »German quote«
	U+00BB	Right-pointing double angle quotation mark	&#187;
	U+2039	Single left-pointing angle quotation mark	&#8249;	‹ x ›
	U+203A	Single right-pointing angle quotation mark	&#8250;
	U+201C	Left double quotation mark	&#8220;	“English quote”
	U+201D	Right double quotation mark	&#8221;
	U+2018	Left single quotation mark	&#8216;	‘English quote’
	U+2019	Right single quotation mark	&#8217;
	U+201A	Single low-9 quotation mark	&#8218; &sbquo;	‚German quote‘ or ‚Polish quote’
	U+201E	Double low-9 quotation mark	&#8222; &bdquo;	„German quote“ or „Polish quote”
Floor and ceiling functions[26]	U+2308	Left ceiling	&#8968;	⌈ceiling⌉
	U+2309	Right ceiling	&#8969;
	U+230A	Left floor	&#8970;	⌊floor⌋
	U+230B	Right floor	&#8971;
Quine corners[26]	U+231C	Top left corner	&#8988;	⌜quasi-quotation⌝ ⌜editorial notation⌝
	U+231D	Top right corner	&#8989;
	U+231E	Bottom left corner	&#8990;	⌞editorial notation⌟
	U+231F	Bottom right corner	&#8991;
Technical/mathematical (specialized)[26][37][38][39]
	U+207D	Superscript left parenthesis	&#8317;	X⁽²⁾
	U+207E	Superscript right parenthesis	&#8318;
	U+208D	Subscript left parenthesis	&#8333;	X₍₂₎
	U+208E	Subscript right parenthesis	&#8334;
	U+239B	Left parenthesis upper hook	&#9115;	⎛ ⎜ ⎝ large parentheses ⎞ ⎟ ⎠
	U+239C	Left parenthesis extension	&#9116;
	U+239D	Left parenthesis lower hook	&#9117;
	U+239E	Right parenthesis upper hook	&#9118;
	U+239F	Right parenthesis extension	&#9119;
	U+23A0	Right parenthesis lower hook	&#9120;
	U+23A1	Left square bracket upper corner	&#9121;	⎡ ⎢ ⎣ large square brackets ⎤ ⎥ ⎦
	U+23A2	Left square bracket extension	&#9122;
	U+23A3	Left square bracket lower corner	&#9123;
	U+23A4	Right square bracket upper corner	&#9124;
	U+23A5	Right square bracket extension	&#9125;
	U+23A6	Right square bracket lower corner	&#9126;
	U+23A7	Left curly bracket upper hook	&#9127;	⎧ ⎨ ⎩ large curly brackets ⎫ ⎬ ⎭
	U+23A8	Left curly bracket middle piece	&#9128;
	U+23A9	Left curly bracket lower hook	&#9129;
	U+23AB	Right curly bracket upper hook	&#9131;
	U+23AC	Right curly bracket middle piece	&#9132;
	U+23AD	Right curly bracket lower hook	&#9133;
	U+23AA	Curly bracket extension	&#9130;	⎪
	U+23B0	Upper left or lower right curly bracket section	&#9136;	⎰ ⎱ more curly brackets ⎱ ⎰
	U+23B1	Upper right or lower left curly bracket section	&#9137;
	U+23B4	Top square bracket	&#9140;	⎴ horizontal square ⎶ brackets ⎵
	U+23B5	Bottom square bracket	&#9141;
	U+23B6	Bottom square bracket over top square bracket	&#9142;
	U+23B8	Left vertical box line	&#9144;	⎸boxed text⎹
	U+23B9	Right vertical box line	&#9145;
	U+23DC	Top parenthesis	&#9180;	⏜ horizontal parentheses ⏝
	U+23DD	Bottom parenthesis	&#9181;
	U+23DE	Top curly bracket	&#9182;	⏞ horizontal curly brackets ⏟
	U+23DF	Bottom curly bracket	&#9183;
	U+23E0	Top tortoise shell bracket	&#9184;	⏠ tortoise shell brackets ⏡
	U+23E1	Bottom tortoise shell bracket	&#9185;
	U+27C5	Left s-shaped bag delimiter	&#10181;	⟅...⟆
	U+27C6	Right s-shaped bag delimiter	&#10182;
	U+27D3	Lower right corner with dot	&#10195;	⟓pullback...pushout⟔
	U+27D4	Upper left corner with dot	&#10196;
	U+27E6	Mathematical left white square bracket	&#10214;	⟦white square brackets⟧
	U+27E7	Mathematical right white square bracket	&#10215;
	U+27E8	Mathematical left angle bracket	&#10216; &lang;[e 1]	⟨a, b⟩
	U+27E9	Mathematical right angle bracket	&#10217; &rang;[e 1]
	U+27EA	Mathematical left double angle bracket	&#10218;	⟪A, B⟫
	U+27EB	Mathematical right double angle bracket	&#10219;
	U+27EC	Mathematical left white tortoise shell bracket	&#10220;	⟬white tortoise shell brackets⟭
	U+27ED	Mathematical right white tortoise shell bracket	&#10221;
	U+27EE	Mathematical left flattened parenthesis	&#10222;	⟮flattened parentheses⟯
	U+27EF	Mathematical right flattened parenthesis	&#10223;
	U+2983	Left white curly bracket	&#10627;	⦃white curly brackets⦄
	U+2984	Right white curly bracket	&#10628;
	U+2985	Left white parenthesis	&#10629;	⦅white/double parentheses⦆
	U+2986	Right white parenthesis	&#10630;
	U+2987	Z notation left image bracket	&#10631;	R⦇S⦈
	U+2988	Z notation right image bracket	&#10632;
	U+2989	Z notation left binding bracket	&#10633;	⦉x:ℤ⦊
	U+298A	Z notation right binding bracket	&#10634;
	U+298B	Left square bracket with underbar	&#10635;	⦋underlined square brackets⦌
	U+298C	Right square bracket with underbar	&#10636;
	U+298D	Left square bracket with tick in top corner	&#10637;	⦍ticked square brackets⦐
	U+2990	Right square bracket with tick in top corner	&#10640;
	U+298E	Right square bracket with tick in bottom corner	&#10638;	⦏ticked square brackets⦎
U+298F	Left square bracket with tick in bottom corner	&#10639;
U+2991	Left angle bracket with dot	&#10641;	⦑dotted angle brackets⦒
U+2992	Right angle bracket with dot	&#10642;
U+2993	Left arc less-than bracket	&#10643;	⦓inequality sign brackets⦔
U+2994	Right arc greater-than bracket	&#10644;
U+2995	Double left arc greater-than bracket	&#10645;	⦕inequality sign brackets⦖
U+2996	Double right arc less-than bracket	&#10646;
U+2997	Left black tortoise shell bracket	&#10647;	⦗black tortoise shell brackets⦘
U+2998	Right black tortoise shell bracket	&#10648;
U+29D8	Left wiggly fence	&#10712;	⧘...⧙
U+29D9	Right wiggly fence	&#10713;
U+29DA	Left double wiggly fence	&#10714;	⧚...⧛
U+29DB	Right double wiggly fence	&#10715;
U+29FC	Left-pointing curved angle bracket	&#10748;	⧼...⧽
U+29FD	Right-pointing curved angle bracket	&#10749;
Half brackets[40]	U+2E22	Top left half bracket	&#11810;	⸢editorial notation⸣
	U+2E23	Top right half bracket	&#11811;
	U+2E24	Bottom left half bracket	&#11812;	⸤editorial notation⸥
	U+2E25	Bottom right half bracket	&#11813;
Dingbats[41]	U+2768	Medium left parenthesis ornament	&#10088;	❨medium parenthesis ornament❩
	U+2769	Medium right parenthesis ornament	&#10089;
	U+276A	Medium flattened left parenthesis ornament	&#10090;	❪medium flattened parenthesis ornament❫
	U+276B	Medium flattened right parenthesis ornament	&#10091;
	U+276C	Medium left-pointing angle bracket ornament	&#10092;	❬medium angle bracket ornament❭
	U+276D	Medium right-pointing angle bracket ornament	&#10093;
	U+2770	Heavy left-pointing angle bracket ornament	&#10096;	❰heavy angle bracket ornament❱
	U+2771	Heavy right-pointing angle bracket ornament	&#10097;
	U+276E	Heavy left-pointing angle quotation mark ornament	&#10094;	❮heavy angle quotation ornament❯
	U+276F	Heavy right-pointing angle quotation mark ornament	&#10095;
	U+2772	Light left tortoise shell bracket ornament	&#10098;	❲light tortoise shell bracket ornament❳
	U+2773	Light right tortoise shell bracket ornament	&#10099;
	U+2774	Medium left curly bracket ornament	&#10100;	❴medium curly bracket ornament❵
	U+2775	Medium right curly bracket ornament	&#10101;
Arabic[42]	U+FD3E	Ornate left parenthesis	&#64830;	﴿العربية﴾‎
	U+FD3F	Ornate right parenthesis	&#64831;
N'Ko[40]	U+2E1C	Left low paraphrase bracket	&#11804;	⸜ߒߞߏ⸝
	U+2E1D	Right low paraphrase bracket	&#11805;
Ogham[43]	U+169B	Ogham feather mark	&#5787;	᚛ᚑᚌᚐᚋ᚜
	U+169C	Ogham reversed feather mark	&#5788;
Old Hungarian	U+2E42	Double low-reversed-9 quotation mark	&#11842;	⹂
Tibetan[44]	U+0F3A	Tibetan mark gug rtags gyon	&#3898;	༺དབུ་ཅན་༻
	U+0F3B	Tibetan mark gug rtags gyas	&#3899;
	U+0F3C	Tibetan mark ang khang gyon	&#3900;	༼༡༢༣༽
	U+0F3D	Tibetan mark ang khang gyas	&#3901;
New Testament editorial marks[40]	U+2E02	Left substitution bracket	&#11778;	⸂...⸃
	U+2E03	Right substitution bracket	&#11779;
	U+2E04	Left dotted substitution bracket	&#11780;	⸄...⸅
	U+2E05	Right dotted substitution bracket	&#11781;
	U+2E09	Left transposition bracket	&#11785;	⸉...⸊
	U+2E0A	Right transposition bracket	&#11786;
	U+2E0C	Left raised omission bracket	&#11788;	⸌...⸍
	U+2E0D	Right raised omission bracket	&#11789;
Medieval studies[36][40]	U+2045	Left square bracket with quill	&#8261;	⁅...⁆
	U+2046	Right square bracket with quill	&#8262;
	U+2E26	Left sideways u bracket	&#11814;	⸦crux⸧
	U+2E27	Right sideways u bracket	&#11815;
	U+2E28	Left double parenthesis	&#11816;	⸨...⸩
	U+2E29	Right double parenthesis	&#11817;
Quotation (East-Asian texts)[45]	U+3014	Left tortoise shell bracket	&#12308;	〔...〕
	U+3015	Right tortoise shell bracket	&#12309;
	U+3016	Left white lenticular bracket	&#12310;	〖...〗
	U+3017	Right white lenticular bracket	&#12311;
	U+3018	Left white tortoise shell bracket	&#12312;	〘...〙
	U+3019	Right white tortoise shell bracket	&#12313;
	U+301A	Left white square bracket	&#12314;	〚...〛
	U+301B	Right white square bracket	&#12315;
	U+301D	Reversed double prime quotation mark	&#12317;	〝...〞
	U+301E	Double prime quotation mark	&#12318;[e 2]
Quotation (halfwidth East-Asian texts)[26][46]	U+2329	Left-pointing angle bracket	&#9001; &lang;[e 1]	〈deprecated〉
	U+232A	Right-pointing angle bracket	&#9002; &rang;[e 1]
	U+FF62	Halfwidth left corner bracket	&#65378;	｢ｶﾀｶﾅ｣
	U+FF63	Halfwidth right corner bracket	&#65379;
Quotation (fullwidth East-Asian texts)[45]	U+3008	Left angle bracket	&#12296;	〈한〉
	U+3009	Right angle bracket	&#12297;
	U+300A	Left double angle bracket	&#12298;	《한》
	U+300B	Right double angle bracket	&#12299;
	U+300C	Left corner bracket	&#12300;	「表題」
	U+300D	Right corner bracket	&#12301;
	U+300E	Left white corner bracket	&#12302;	『表題』
	U+300F	Right white corner bracket	&#12303;
	U+3010	Left black lenticular bracket	&#12304;	【表題】
	U+3011	Right black lenticular bracket	&#12305;
General purpose (fullwidth East-Asian)[46]	U+FF08	Fullwidth left parenthesis	&#65288;	（Ｗｉｋｉ）
	U+FF09	Fullwidth right parenthesis	&#65289;
	U+FF3B	Fullwidth left square bracket	&#65339;	［ｓｉｃ］
	U+FF3D	Fullwidth right square bracket	&#65341;
Technical/mathematical (fullwidth East-Asian)[46]	U+FF1C	Fullwidth less-than sign	&#65308;	＜ＨＴＭＬ＞
	U+FF1E	Fullwidth greater-than sign	&#65310;
	U+FF5B	Fullwidth left curly bracket	&#65371;	｛１、２｝
	U+FF5D	Fullwidth right curly bracket	&#65373;
	U+FF5F	Fullwidth left white parenthesis	&#65375;	｟...｠
	U+FF60	Fullwidth right white parenthesis	&#65376;

1. &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.
2. This is fullwidth version of U+2033 DOUBLE PRIME. In vertical texts, U+301F LOW DOUBLE PRIME QUOTATION MARK is preferred.

Braces (curly brackets) first became part of a character set with the 8-bit code of the IBM 7030 Stretch.[47]

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,[26] 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.

See also

• International variation in quotation marks
• Emoticon
• Japanese typographic symbols
• Order of operations

References

1. "Unicode Bidirectional Algorithm: 3.1.3 Paired Brackets". Unicode Technical Reports. Retrieved 24 April 2018.
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. "broket". Catb.org. Retrieved 13 February 2013.
6. Merriam-Webster's Manual for Writers and Editors. Merriam-Webster. 1998. p. 149. ISBN 0-87779-622-X – via Google Books.
7. Robert Bringhurst, The Elements of Typographic Style, §5.3.2.
8. Forsmann, Friedrich; DeJong, Ralf (2004). Detailtypografie [Detail Typography] (in German). Mainz: Herrmann Schmidt. p. 263. ISBN 978-3874396424.
9. Straus, Jane. "Parentheses—Punctuation Rules". The Blue Book of Grammar and Punctuation. grammarbook.com. Retrieved 18 April 2014.
10. Slash (punctuation)#Gender-neutrality in Spanish and Portuguese
11. "The Free Online Dictionary". Thefreedictionary.com. Retrieved 13 February 2013.
12. "Archived copy". Archived from the original on 6 August 2014. Retrieved 1 August 2014.CS1 maint: archived copy as title (link)
13. "Standard Uncertainty and Relative Standard Uncertainty". CODATA reference. NIST. Retrieved 20 July 2018.
14. The Chicago Manual of Style, 15th ed., The University of Chicago Press, 2003, §6.104
15. "Bartleby.com: Great Books Online – Quotes, Poems, Novels, Classics and hundreds more". bartleby.com. Archived from the original on 24 May 2008.
16. The Chicago Manual of Style, 15th ed., The University of Chicago Press, 2003, §6.102 and §6.106
17. The Chicago Manual of Style, 15th ed., The University of Chicago Press, 2003, §6.105
18. The Chicago Manual of Style, 15th ed., The University of Chicago Press, 2003, §6.107
19. "Are curly braces ever used in normal text? If not, why were they created?". Stack Exchange. Retrieved 24 April 2018.
20. "> U+007B LEFT CURLY BRACKET". Decodeunicode.org. Archived from the original on 2 December 2008.
21. "Brace and Indent Styles and Code Convention". riedquat.de. Archived from the original on 24 September 2015.
22. Bauer, Laurie (2007). "Notational conventions. Brackets". The Linguistics Student's Handbook. Edinburgh: Edinburgh University Press. p. 99. ISBN 9780748627592.
23. Sampson, Geoffrey (2016). "Writing systems: methods for recording language". In Allan, Keith (ed.). The Routledge Handbook of Linguistics. Routledge. p. 60. ISBN 9781317513049.
24. Trask, Robert Lawrence (2000). "Angle brackets". The Dictionary of Historical and Comparative Linguistics. Edinburgh: Edinburgh University Press. p. 22. ISBN 9781579582180.
25. M.L. West (1973) Textual Criticism and Editorial Technique (Stuttgart) 81.
26. "Miscellaneous Technical Code Chart" (PDF), The Unicode Standard, retrieved 27 February 2016
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, Oxford University Computing Laboratory, Programming Research Group.
29. "Text Leiden+ Documentation". Papyri.info.
30. Examples may be found under the corresponding entry at :sv:Parentes.
31. Brian W. Kernighan, Dennis M. Ritchie. "The C Programming Language", 1988. p. 7. ISBN 0-13-110370-9
32. Bjarne Stroustrup, "The C++ Programming Language", 2013. p.39. ISBN 0-13-352285-7
33. California Style Manual, section 4:59 (4th ed.)
34. "C0 Controls and Basic Latin Code Chart" (PDF), The Unicode Standard, retrieved 27 February 2016
35. "C1 Controls and Latin-1 Supplement Code Chart" (PDF), The Unicode Standard, retrieved 27 February 2016
36. "General Punctuation Code Chart" (PDF), The Unicode Standard, retrieved 1 March 2016
37. "Superscripts and Subscripts Code Chart" (PDF), The Unicode Standard, retrieved 27 February 2016
38. "Miscellaneous Mathematical Symbols-A Code Chart" (PDF), The Unicode Standard, retrieved 27 February 2016
39. "Miscellaneous Mathematical Symbols-B Code Chart" (PDF), The Unicode Standard, retrieved 27 February 2016
40. "Supplemental Punctuation Code Chart" (PDF), The Unicode Standard, retrieved 27 February 2016
41. "Dingbats Code Chart" (PDF), The Unicode Standard, retrieved 27 February 2016
42. "Arabic Presentation Forms-A Code Chart" (PDF), The Unicode Standard, retrieved 27 February 2016
43. "Ogham Code Chart" (PDF), The Unicode Standard, retrieved 27 February 2016
44. "Tibetan Code Chart" (PDF), The Unicode Standard, retrieved 27 February 2016
45. "CJK Symbols and Punctuation Code Chart" (PDF), The Unicode Standard, retrieved 27 February 2016
46. "Halfwidth and Fullwidth Forms Code Chart" (PDF), The Unicode Standard, retrieved 27 February 2016
47. Bob, Bemer. "The Great Curly Brace Trace Chase". Archived from the original on 3 September 2009. Retrieved 5 September 2009.

Bibliography

• Lennard, John (1991). But I Digress: The Exploitation of Parentheses in English Printed Verse. Oxford: Clarendon Press. ISBN 0-19-811247-5.
• Turnbull; et al. (1964). The Graphics of Communication. New York: Holt. 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

• Media related to Brackets at Wikimedia Commons
• The dictionary definition of bracket at Wiktionary