# 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 bracket or closing bracket,[1] respectively, depending on the directionality of the context.

Brackets
( ) [ ] { }
Round brackets
or
parentheses
Square brackets
or
brackets
Curly brackets
or
braces
Angle brackets
or
chevrons

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 most English-speaking countries, an unqualified 'bracket' refers to the round bracket; in the United States, the square bracket.

Various forms of brackets are used in mathematics, with specific mathematical meanings, often for denoting specific mathematical functions and subformulas.

## 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]

Most typewriters only had parenthesis (and quotes). Square brackets appeared with some teleprinters.

Braces (curly brackets) first became part of a character set with the 8-bit code of the IBM 7030 Stretch.[3]

In 1961, ASCII contained parenthesis, square, and curly brackets, and also less-than and greater-than signs that could be used as angle brackets.

## Typography

In English, typographers mostly prefer not to set brackets in italics, even when the enclosed text is italic.[4] However, in other languages like German, if brackets enclose text in italics, they are usually also set in italics.[5]

## Parentheses

Parenthesis
( )

Parentheses /pəˈrɛnθɪsz/ (singular, parenthesis /pəˈrɛnθɪsɪs/) are also called "brackets" (UK, Ireland, Canada, West Indies, New Zealand, South Africa and Australia), "parens" /pəˈrɛnz/, "round brackets", "circle brackets" or "smooth brackets".

### Uses of ( )

Parentheses contain adjunctive material that serves to clarify (in the manner of a gloss) or is aside from the main point.[6] 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 "Senator 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).[7]

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 use, 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").[8]

#### Enumerations

An unpaired right parenthesis is often used as part of a label in an ordered list:

a) educational testing,
b) technical writing and diagrams,
c) market research, and
d) elections.

#### Accounting

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

#### Parentheses 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.[9]

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

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.

#### Parentheses 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, such as in extended Backus–Naur form.

#### Taxonomy

If it is desired to include the subgenus when giving the scientific name of an animal species or subspecies, the subgenus's name is provided in parentheses between the genus name and the specific epithet.[10] For instance, Polyphylla (Xerasiobia) alba is a way to cite the species Polyphylla alba while also mentioning that it's in the subgenus Xerasiobia.[11] There is also a convention of citing a subgenus by enclosing it in parentheses after its genus, e.g., Polyphylla (Xerasiobia) is a way to refer to the subgenus Xerasiobia within the genus Polyphylla.[12] Parentheses are similarly used to cite a subgenus with the name of a prokaryotic species, although the International Code of Nomenclature of Prokaryotes (ICNP) requires the use of the abbreviation "subgen." as well, e.g., Acetobacter (subgen. Gluconoacetobacter) liquefaciens.[13]

In some contexts, it is typical to cite the author's name alongside the taxon. In these contexts, parentheses mean that the author placed that species in a different genus from the one in that combination. The International Code of Zoological Nomenclature gives the example of Hymenolepis diminuta (Rudolphi, 1819) to indicate that Karl Rudolphi did not consider this species to be in the genus Hymenolepis when he first described the species. The author citation in zoology also allows the possibility of citing whoever transferred the species to the new genus, as in, Methiolopsis geniculata (Stål, 1878) Rehn, 1957.[14] Parentheses are similarly used for new combinations of prokaryotes as well; the ICNP provides the example: Microbacterium oxydans (Chatelain and Second 1966) Schumann et al. 1999 to indicate that Chatelain and Second first described the species in a different genus, namely Brevibacterium, but in 1999 Schumann and colleagues transferred it to its present genus.[15] Author citations in botany also use parentheses in this way where the author (or abbreviation thereof) of the basionym is in parentheses followed by the author (or abbreviation thereof) of whoever created that particular combination; the International Code of Nomenclature for algae, fungi, and plants provides the example Helianthemum aegyptiacum (L.) Mill. to indicate that Carl Linnaeus first described this species in a different genus, in this case Cistus, but then Philip Miller transferred it to the genus Helianthemum.[16]

#### Chemistry and physics

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:[17]

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

Square brackets
[ ]

Square brackets [ and ] are also called simply "brackets" (US), as well as "crotchets", "closed brackets", or "hard brackets".[18]

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

### Uses of [ ]

Square brackets are often used to insert explanatory material or to mark where a [word or] passage was omitted from an original material by someone other than the original author, or to mark modifications in quotations.[19] In transcribed interviews, sounds, responses and reactions that are not words but that can be described are set off in square brackets — "... [laughs] ...".

When quoted material is in any way altered, the alterations are enclosed in square brackets within the quotation to show that the quotation is not exactly as given, or to add an annotation.[20] 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').

A bracketed ellipsis, [...], is often used to indicate omitted material: "I'd like to thank [several unimportant people] for their tolerance [...]"[21] 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.[22] 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".[23]

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.[24] For example: He is trained in the way of the open hand [karate].

Style and usage guides originating in the news industry of the twentieth century, such as the AP Stylebook, recommend against the use of square brackets because "They cannot be transmitted over news wires."[25] However, this guidance has little relevance outside of the technological constraints of the industry and era.

In linguistics, phonetic transcriptions are generally enclosed within square brackets,[26] often using the International Phonetic Alphabet#Brackets and transcription delimiters, 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 (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. ]Paradise Lost[

Square brackets are used to denote parts of the text that need to be checked when preparing drafts prior to finalizing a document.

#### Law

Square brackets are used in some countries in the citation of law 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

This case is in the 1954 volume of the Appeal Cases reports, although the decision may have been given in 1953 or earlier. Compare with:

(1954) 98 Sol Jo 176

This citation reports a decision from 1954, in volume 98 of the Solicitors Journal which may be published in 1955 or later.

They often denote points that have not yet been agreed to in legal drafts and the year in which a report was made for certain case law decisions.

#### Square brackets in mathematics

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 represent intervals; [0,5] for example, represents the set of real numbers from 0 to 5 inclusive. Both parentheses and brackets are used to denote a half-open interval; [5, 12) would be the set of all real numbers between 5 and 12, including 5 but not 12. The numbers may come as close as they like to 12, including 11.999 and so forth, but 12.0 is not included. In some European countries, the notation [5, 12[ is also used. The endpoint adjoining the square bracket is known as closed, whereas the endpoint adjoining the parenthesis is known as open.

In group theory and ring theory, brackets denote the commutator. In group theory, the commutator [g, h] is commonly defined as g −1h −1gh. In ring theory, the commutator [a, b] is defined as abba.

#### Chemistry

Square brackets can also be used in chemistry to represent the concentration of a chemical substance in solution and to denote charge a Lewis structure of an ion (particularly distributed charge in a complex ion), repeating chemical units (particularly in polymers) and transition state structures, among other uses.

#### Square brackets in programming languages

Brackets are used in many computer programming languages, primarily for 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 portions, such as in extended Backus–Naur form.

## Curly brackets

Curly brackets
{ }
An example of curly brackets used to group sentences together

Curly brackets { and } are also known as "curly braces" or simply "braces"[27] (UK and US), "definite brackets", "swirly brackets", "birdie brackets", "French brackets", "Scottish brackets", "squirrelly brackets", "gullwings", "seagulls", "squiggly brackets", "twirly brackets", "Tuborg brackets" (DK), "accolades" (NL), "pointy brackets", "fancy brackets", "M Braces", "moustache brackets", "squiggly parentheses", or "flower brackets" (India).

### Uses of { }

Curly brackets 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). More commonly, they are used to indicate a group of lines that should be taken together, such as in when referring to several lines of poetry that should be repeated.[28]

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

#### Music

In music, they are known as "accolades" or "braces", and connect two or more lines (staves) of music that are played simultaneously.[29]

#### Curly brackets in programming languages

In many programming languages, curly brackets enclose groups of statements and create a local scope. Such languages (C, C#, C++ and many others) are therefore called curly bracket languages.[30] They are also used to define structures and enumerated type in these languages.

In syntax diagrams they are used for repetition, such as in extended Backus–Naur form.

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

#### Curly brackets in mathematics

In mathematics they delimit sets and are often also used to denote the Poisson bracket between two quantities.

In ring theory, braces denote the anticommutator where {a, b} is defined as ab + ba.

## Angle brackets

Angle brackets

"Angle brackets" ⟨ and ⟩ are also called "chevrons", "pointy brackets", "triangular brackets", "diamond brackets", "tuples", "guillemets", "left and right carrot", "broken brackets", or "brokets".[31]

The ASCII less-than and greater-than characters <> are often used for chevrons. In most cases only those characters are accepted by computer programs, the Unicode chevrons are not recognized (for instance in HTML tags). The characters for "single" guillemets ‹› are also often used, and sometimes normal guillemets «» when nested chevrons are needed.

### Uses of ⟨ ⟩

Chevrons 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.[32]

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 linguistics, angle brackets identify graphemes (e.g., letters of an alphabet) or orthography, as in "The English word /kæt/ is spelled cat."[33][34][32]

In epigraphy, they may be used for mechanical transliterations of a text into the Latin script.[34]

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.

#### Angle brackets in mathematics

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[35] 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 over time or over another continuous parameter. For example:

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

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

In C++ chevrons (actually less-than and greater-than) are used to surround arguments to templates.

In the Z formal specification language chevrons define a sequence.

In HTML, chevrons (actually 'greater than' 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 use is sometimes extended as an informal mechanism for communicating mood or tone in digital formats such as messaging, for example adding "<sighs>" at the end of a sentence.

## Other brackets

### 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 in titles and headings in both Chinese[36] and Japanese. In Japanese, they are most frequently seen in dictionaries for quoting Chinese characters and Sino-Japanese loanwords.

### 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.[37] 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.[38]

### Double brackets

Double brackets (or white square brackets or Scott brackets), ⟦ ⟧, are used to indicate the semantic evaluation function in formal semantics for natural language and denotational semantics for programming languages.[39][40] 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.[41]

### Brackets with quills

Known as "spike parentheses" (Swedish: piggparenteser), ⁅ and ⁆ are used in Swedish bilingual dictionaries to enclose supplemental constructions.[42]

## Unicode

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

UsesUnicodeSGML/HTML/XML entitiesSample
General purpose[43] U+0028Left parenthesis&#40; &lparen;(parentheses)
U+0029Right parenthesis&#41; &rparen;
U+005BLeft square bracket&#91;[sic]
U+005DRight square bracket&#93;
Technical/mathematical
(common)[43]
U+003CLess-than sign&#60; &lt;<HTML>
U+003EGreater-than sign&#62; &gt;
U+007BLeft curly bracket&#123;{round, square, curly}
U+007DRight curly bracket&#125;
Quotation
(Western texts)[44][45]
U+00ABLeft-pointing double angle quotation mark&#171;«Spanish quote», « French quote » or »German quote«
U+00BBRight-pointing double angle quotation mark&#187;
U+2039Single left-pointing angle quotation mark&#8249;‹ x ›
U+203ASingle right-pointing angle quotation mark&#8250;
U+201CLeft double quotation mark&#8220;“English quote”
U+201DRight double quotation mark&#8221;
U+2018Left single quotation mark&#8216;‘English quote’
U+2019Right single quotation mark&#8217;
U+201ASingle low-9 quotation mark&#8218; &sbquo;‚German quote‘ or ‚Polish quote’
U+201EDouble low-9 quotation mark&#8222; &bdquo;„German quote“ or „Polish quote”
Floor and ceiling functions[38] U+2308Left ceiling&#8968;ceiling
U+2309Right ceiling&#8969;
U+230ALeft floor&#8970;floor
U+230BRight floor&#8971;
Quine corners[38] U+231CTop left corner&#8988;quasi-quotation
editorial notation
U+231DTop right corner&#8989;
U+231EBottom left corner&#8990;editorial notation
U+231FBottom right corner&#8991;
Technical/mathematical
(specialized)[38][46][47][48]
U+207DSuperscript left parenthesis&#8317;X⁽²⁾
U+207ESuperscript right parenthesis&#8318;
U+208DSubscript left parenthesis&#8333;X₍₂₎
U+208ESubscript right parenthesis&#8334;
U+239BLeft parenthesis upper hook&#9115;

large

parentheses

U+239CLeft parenthesis extension&#9116;
U+239DLeft parenthesis lower hook&#9117;
U+239ERight parenthesis upper hook&#9118;
U+239FRight parenthesis extension&#9119;
U+23A0Right parenthesis lower hook&#9120;
U+23A1Left square bracket upper corner&#9121;

large
square
brackets

U+23A2Left square bracket extension&#9122;
U+23A3Left square bracket lower corner&#9123;
U+23A4Right square bracket upper corner&#9124;
U+23A5Right square bracket extension&#9125;
U+23A6Right square bracket lower corner&#9126;
U+23A7Left curly bracket upper hook&#9127;

large
curly
brackets

U+23A8Left curly bracket middle piece&#9128;
U+23A9Left curly bracket lower hook&#9129;
U+23ABRight curly bracket upper hook&#9131;
U+23ACRight curly bracket middle piece&#9132;
U+23AACurly bracket extension&#9130;
U+23B0Upper left or lower right curly bracket section&#9136;

more curly
brackets

U+23B1Upper right or lower left curly bracket section&#9137;
U+23B4Top square bracket&#9140;

horizontal square

brackets

U+23B5Bottom square bracket&#9141;
U+23B6Bottom square bracket over top square bracket&#9142;
U+23B8Left vertical box line&#9144;⎸boxed text⎹
U+23B9Right vertical box line&#9145;
U+23DCTop parenthesis&#9180;

horizontal parentheses

U+23DDBottom parenthesis&#9181;
U+23DETop curly bracket&#9182;

horizontal curly brackets

U+23DFBottom curly bracket&#9183;
U+23E0Top tortoise shell bracket&#9184;

tortoise shell brackets

U+23E1Bottom tortoise shell bracket&#9185;
U+27C5Left s-shaped bag delimiter&#10181;⟅...⟆
U+27C6Right s-shaped bag delimiter&#10182;
U+27D3Lower right corner with dot&#10195;⟓pullback...pushout⟔
U+27D4Upper left corner with dot&#10196;
U+27E6Mathematical left white square bracket&#10214;⟦white square brackets⟧
U+27E7Mathematical right white square bracket&#10215;
U+27E8Mathematical left angle bracket&#10216; &lang;[e 1]a, b
U+27E9Mathematical right angle bracket&#10217; &rang;[e 1]
U+27EAMathematical left double angle bracket&#10218;A, B
U+27EBMathematical right double angle bracket&#10219;
U+27ECMathematical left white tortoise shell bracket&#10220;⟬white tortoise shell brackets⟭
U+27EDMathematical right white tortoise shell bracket&#10221;
U+27EEMathematical left flattened parenthesis&#10222;⟮flattened parentheses⟯
U+27EFMathematical right flattened parenthesis&#10223;
U+2983Left white curly bracket&#10627;⦃white curly brackets⦄
U+2984Right white curly bracket&#10628;
U+2985Left white parenthesis&#10629;⦅white/double parentheses⦆
U+2986Right white parenthesis&#10630;
U+2987Z notation left image bracket&#10631;RS
U+2988Z notation right image bracket&#10632;
U+2989Z notation left binding bracket&#10633;x:ℤ
U+298AZ notation right binding bracket&#10634;
U+298BLeft square bracket with underbar&#10635;⦋underlined square brackets⦌
U+298CRight square bracket with underbar&#10636;
U+298DLeft square bracket with tick in top corner&#10637;⦍ticked square brackets⦐
U+2990Right square bracket with tick in top corner&#10640;
U+298ERight square bracket with tick in bottom corner&#10638;⦏ticked square brackets⦎
U+298FLeft square bracket with tick in bottom corner&#10639;
U+2991Left angle bracket with dot&#10641;⦑dotted angle brackets⦒
U+2992Right angle bracket with dot&#10642;
U+2993Left arc less-than bracket&#10643;inequality sign brackets⦔
U+2994Right arc greater-than bracket&#10644;
U+2995Double left arc greater-than bracket&#10645;⦕inequality sign brackets⦖
U+2996Double right arc less-than bracket&#10646;
U+2997Left black tortoise shell bracket&#10647;⦗black tortoise shell brackets⦘
U+2998Right black tortoise shell bracket&#10648;
U+29D8Left wiggly fence&#10712;⧘...⧙
U+29D9Right wiggly fence&#10713;
U+29DALeft double wiggly fence&#10714;⧚...⧛
U+29DBRight double wiggly fence&#10715;
U+29FCLeft-pointing curved angle bracket&#10748;⧼...⧽
U+29FDRight-pointing curved angle bracket&#10749;
Half brackets[49] U+2E22Top left half bracket&#11810;editorial notation
U+2E23Top right half bracket&#11811;
U+2E24Bottom left half bracket&#11812;editorial notation
U+2E25Bottom right half bracket&#11813;
Dingbats[50] U+2768Medium left parenthesis ornament&#10088;❨medium parenthesis ornament❩
U+2769Medium right parenthesis ornament&#10089;
U+276AMedium flattened left parenthesis ornament&#10090;❪medium flattened parenthesis ornament❫
U+276BMedium flattened right parenthesis ornament&#10091;
U+276CMedium left-pointing angle bracket ornament&#10092;❬medium angle bracket ornament❭
U+276DMedium right-pointing angle bracket ornament&#10093;
U+2770Heavy left-pointing angle bracket ornament&#10096;❰heavy angle bracket ornament❱
U+2771Heavy right-pointing angle bracket ornament&#10097;
U+276EHeavy left-pointing angle quotation mark ornament&#10094;❮heavy angle quotation ornament❯
U+276FHeavy right-pointing angle quotation mark ornament&#10095;
U+2772Light left tortoise shell bracket ornament&#10098;❲light tortoise shell bracket ornament❳
U+2773Light right tortoise shell bracket ornament&#10099;
U+2774Medium left curly bracket ornament&#10100;❴medium curly bracket ornament❵
U+2775Medium right curly bracket ornament&#10101;
Arabic (Quranic quotations)[51] U+FD3EOrnate left parenthesis&#64830;﴿قُلْ صَدَقَ ٱللَّهُ﴾
U+FD3FOrnate right parenthesis&#64831;
N'Ko[49] U+2E1CLeft low paraphrase bracket&#11804;⸜ߒߞߏ⸝
U+2E1DRight low paraphrase bracket&#11805;
Ogham[52] U+169BOgham feather mark&#5787;᚛ᚑᚌᚐᚋ᚜
U+169COgham reversed feather mark&#5788;
Old HungarianU+2E42Double low-reversed-9 quotation mark&#11842;
Tibetan[53] U+0F3ATibetan mark gug rtags gyon&#3898;༺དབུ་ཅན་༻
U+0F3BTibetan mark gug rtags gyas&#3899;
U+0F3CTibetan mark ang khang gyon&#3900;༼༡༢༣༽
U+0F3DTibetan mark ang khang gyas&#3901;
New Testament editorial marks[49] U+2E02Left substitution bracket&#11778;⸂...⸃
U+2E03Right substitution bracket&#11779;
U+2E04Left dotted substitution bracket&#11780;⸄...⸅
U+2E05Right dotted substitution bracket&#11781;
U+2E09Left transposition bracket&#11785;⸉...⸊
U+2E0ARight transposition bracket&#11786;
U+2E0CLeft raised omission bracket&#11788;⸌...⸍
U+2E0DRight raised omission bracket&#11789;
Medieval studies[45][49] U+2045Left square bracket with quill&#8261;⁅...⁆
U+2046Right square bracket with quill&#8262;
U+2E26Left sideways u bracket&#11814;⸦crux⸧
U+2E27Right sideways u bracket&#11815;
U+2E28Left double parenthesis&#11816;⸨...⸩
U+2E29Right double parenthesis&#11817;
Quotation
(East-Asian texts)[54]
U+3014Left tortoise shell bracket&#12308;〔...〕
U+3015Right tortoise shell bracket&#12309;
U+3016Left white lenticular bracket&#12310;〖...〗
U+3017Right white lenticular bracket&#12311;
U+3018Left white tortoise shell bracket&#12312;〘...〙
U+3019Right white tortoise shell bracket&#12313;
U+301ALeft white square bracket&#12314;〚...〛
U+301BRight white square bracket&#12315;
U+301DReversed double prime quotation mark&#12317;〝...〞
U+301EDouble prime quotation mark&#12318;[e 2]
Quotation
(halfwidth East-Asian texts)[38][55]
U+2329Left-pointing angle bracket&#9001; &lang;[e 1]〈deprecated〉
U+232ARight-pointing angle bracket&#9002; &rang;[e 1]
U+FF62Halfwidth left corner bracket&#65378;｢ｶﾀｶﾅ｣
U+FF63Halfwidth right corner bracket&#65379;
Quotation
(fullwidth East-Asian texts)[54]
U+3008Left angle bracket&#12296;〈한〉
U+3009Right angle bracket&#12297;
U+300ALeft double angle bracket&#12298;《한》
U+300BRight double angle bracket&#12299;
U+300CLeft corner bracket&#12300;「表題」
U+300DRight corner bracket&#12301;
U+300ELeft white corner bracket&#12302;『表題』
U+300FRight white corner bracket&#12303;
U+3010Left black lenticular bracket&#12304;【表題】
U+3011Right black lenticular bracket&#12305;
General purpose
(fullwidth East-Asian)[55]
U+FF08Fullwidth left parenthesis&#65288;（Ｗｉｋｉ）
U+FF09Fullwidth right parenthesis&#65289;
U+FF3BFullwidth left square bracket&#65339;ｓｉｃ
U+FF3DFullwidth right square bracket&#65341;
Technical/mathematical
(fullwidth East-Asian)[55]
U+FF1CFullwidth less-than sign&#65308;＜ＨＴＭＬ＞
U+FF1EFullwidth greater-than sign&#65310;
U+FF5BFullwidth left curly bracket&#65371;｛１、２｝
U+FF5DFullwidth right curly bracket&#65373;
U+FF5FFullwidth left white parenthesis&#65375;｟...｠
U+FF60Fullwidth 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.

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,[38] 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.

## 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. Bob, Bemer. "The Great Curly Brace Trace Chase". Archived from the original on 3 September 2009. Retrieved 5 September 2009.
4. Robert Bringhurst, The Elements of Typographic Style, §5.3.2.
5. Forsmann, Friedrich; DeJong, Ralf (2004). Detailtypografie [Detail Typography] (in German). Mainz: Herrmann Schmidt. p. 263. ISBN 978-3874396424.
6. Straus, Jane. "Parentheses—Punctuation Rules". The Blue Book of Grammar and Punctuation. grammarbook.com. Retrieved 18 April 2014.
7. Slash (punctuation)#Gender-neutrality in Spanish and Portuguese
8. "The Free Online Dictionary". Thefreedictionary.com. Retrieved 13 February 2013.
9. "Archived copy". Archived from the original on 6 August 2014. Retrieved 1 August 2014.CS1 maint: archived copy as title (link)
10. International Commission on Zoological Nomenclature (2012). "6.1. Names of subgenera". International Code of Zoological Nomenclature (4th ed.). Retrieved 6 June 2021.
11. Welter-Schultes, Francisco W. (March 2013). "1.4.5.4 Species". Guidelines for the Capture and Management of Digital Zoological Names Information. Copenhagen: Global Biodiversity Information Facility. pp. 14–15. ISBN 978-87-92020-44-4.
12. Welter-Schultes, Francisco W. (March 2013). "1.4.5.3 Genera". Guidelines for the Capture and Management of Digital Zoological Names Information. Copenhagen: Global Biodiversity Information Facility. p. 14. ISBN 978-87-92020-44-4.
13. Parker, Charles T.; Tindall, Brian J.; Garrity, George M., eds. (2019). "International Code of Nomenclature of Prokaryotes: Prokaryotic Code (2008 Revision)". International Journal of Systematic and Evolutionary Microbiology. 69 (1A): S19. doi:10.1099/ijsem.0.000778. PMID 26596770.
14. International Commission on Zoological Nomenclature (2012). "Article 51. Citation of names of authors". International Code of Zoological Nomenclature (4th ed.). Retrieved 6 June 2021.
15. Parker, Charles T.; Tindall, Brian J.; Garrity, George M., eds. (2019). "International Code of Nomenclature of Prokaryotes: Prokaryotic Code (2008 Revision)". International Journal of Systematic and Evolutionary Microbiology. 69 (1A): S32. doi:10.1099/ijsem.0.000778. PMID 26596770.
16. Nineteenth International Botanical Congress (2018). "Article 49". International Code of Nomenclature for algae, fungi, and plants (Shenzhen Code). Koeltz Botanical Books. Retrieved 7 June 2021.
17. "Standard Uncertainty and Relative Standard Uncertainty". CODATA reference. NIST. Retrieved 20 July 2018.
18. Smith, John. The Printer’s Grammar p. 84.
19. The Chicago Manual of Style, 15th ed., The University of Chicago Press, 2003, §6.104
20. California Style Manual, section 4:59 (4th ed.)
21. "Bartleby.com: Great Books Online – Quotes, Poems, Novels, Classics and hundreds more". bartleby.com. Archived from the original on 24 May 2008.
22. The Chicago Manual of Style, 15th ed., The University of Chicago Press, 2003, §6.102 and §6.106
23. How to Integrate Direct Quotations into Your Writing. University of Washington. 2004.
24. The Chicago Manual of Style, 15th ed., The University of Chicago Press, 2003, §6.105
25. Christian, Darrell; Froke, Paula Marie; Jacobsen, Sally A.; Minthorn, David, eds. (2014). "brackets []". Associated Press Stylebook 2014. AP Stylebook 2014. Chapter "Punctuation Guide" (49th ed.). New York: Associated Press. p. 289. ISBN 9780917360589. LCCN 2002249088. OCLC 881182354.
26. The Chicago Manual of Style, 15th ed., The University of Chicago Press, 2003, §6.107
27. Concise Oxford Dictionary, 10th Edition, Oxford University Press, Great Clarendon Street, Oxford OX2 2DP, UK
28. "Are curly braces ever used in normal text? If not, why were they created?". Stack Exchange. Retrieved 24 April 2018. A sign } used in writing or printing, chiefly for the purpose of uniting together two or more lines, words, staves of music, etc. Sometimes, but less correctly, used in plural to denote square brackets [ ].
29. "> U+007B LEFT CURLY BRACKET". Decodeunicode.org. Archived from the original on 2 December 2008.
30. "Brace and Indent Styles and Code Convention". riedquat.de. Archived from the original on 24 September 2015.
31. "broket". Catb.org. Retrieved 13 February 2013.
32. Trask, Robert Lawrence (2000). "Angle brackets". The Dictionary of Historical and Comparative Linguistics. Edinburgh: Edinburgh University Press. p. 22. ISBN 9781579582180.
33. Bauer, Laurie (2007). "Notational conventions. Brackets". The Linguistics Student's Handbook. Edinburgh: Edinburgh University Press. p. 99. ISBN 9780748627592.
34. Sampson, Geoffrey (2016). "Writing systems: methods for recording language". In Allan, Keith (ed.). The Routledge Handbook of Linguistics. Routledge. p. 60. ISBN 9781317513049.
35. Hefferon, Jim. Linear algebra (PDF). p. 121.
36. GB/T 15834-2011 标点符号用法(General rules for punctuation), 30 December 2011, 4.9.3.3, 4.9.3.5
37. M.L. West (1973) Textual Criticism and Editorial Technique (Stuttgart) 81.
38. "Miscellaneous Technical Code Chart" (PDF), The Unicode Standard, retrieved 27 February 2016
39. Dowty, D., Wall, R. and Peters, S.: 1981, Introduction to Montague semantics, Springer.
40. Scott, D. and Strachey, C.: 1971, Toward a mathematical semantics for computer languages, Oxford University Computing Laboratory, Programming Research Group.
41. "Text Leiden+ Documentation". Papyri.info.
42. Examples may be found under the corresponding entry at :sv:Parentes.
43. "C0 Controls and Basic Latin Code Chart" (PDF), The Unicode Standard, retrieved 27 February 2016
44. "C1 Controls and Latin-1 Supplement Code Chart" (PDF), The Unicode Standard, retrieved 27 February 2016
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48. "Miscellaneous Mathematical Symbols-B Code Chart" (PDF), The Unicode Standard, retrieved 27 February 2016
49. "Supplemental Punctuation Code Chart" (PDF), The Unicode Standard, retrieved 27 February 2016
50. "Dingbats Code Chart" (PDF), The Unicode Standard, retrieved 27 February 2016
51. "Arabic Presentation Forms-A Code Chart" (PDF), The Unicode Standard, retrieved 27 February 2016
52. "Ogham Code Chart" (PDF), The Unicode Standard, retrieved 27 February 2016
53. "Tibetan Code Chart" (PDF), The Unicode Standard, retrieved 27 February 2016
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## 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.