Bracket

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).

"( )" redirects here. For the Sigur Rós album, see ( ) (album). For other uses, see ( ) (disambiguation).

[ ]

Brackets

( )	{ }	〈〉
Round brackets or parentheses	Curly brackets or braces	Angle brackets or chevrons

A bracket is a tall punctuation mark typically used in matched pairs within text, to set apart or interject other text. Used unqualified, brackets refer to different types of brackets in different parts of the world and in different contexts. The matched pair may be described as opening and closing,^[1] or left and right symbols.

Brackets include round brackets/parentheses, square brackets, curly brackets/braces, angle brackets, and 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 parenthesis.

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

Some of the following names are regional or contextual.

( ) – parentheses, brackets (UK, Canada, New Zealand, South Africa and Australia), parens, round brackets, soft brackets, first brackets or circle brackets
[ ] – square brackets, closed brackets, hard brackets, second brackets, crotchets,^[3] or brackets (US)
{ } – braces are "two connecting marks used in printing"; and in music "to connect staves to be performed at the same time"^[4] (UK and US), flower brackets (India), French brackets, curly brackets, definite brackets, swirly brackets, curly braces, birdie brackets, Scottish brackets, squirrelly brackets, gullwings, seagulls, squiggly brackets, twirly brackets, Tuborg brackets (DK), accolades (NL), pointy brackets, third brackets, or fancy brackets
〈〉– pointy brackets, angle brackets, triangular brackets, diamond brackets, tuples, or chevrons
< > – inequality signs, pointy brackets, or brackets. Sometimes referred to as angle brackets, in such cases as HTML markup. Occasionally known as broken brackets or brokets.^[5]
⸤ ⸥; ｢｣ – corner brackets
⟦ ⟧ – double square brackets, white square brackets
Guillemets, ‹ › and « », are sometimes referred to as chevrons or [double] angle brackets.^[1]

Typography

The characters ‹ › and « », known as guillemets or angular quote brackets, are actually quotation mark glyphs 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.

In English, typographers generally prefer to not 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 set in italics too.^[8]

Types and uses

Parentheses

Various terms redirect here; for other uses, see Parenthesis (disambiguation), ( ) (disambiguation), Parenthetical referencing, and Parenthetical Girls

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

Parentheses /pəˈrɛnθᵻsiːz/ (singular, parenthesis /pəˈrɛnθᵻsᵻs/) (also called simply brackets, or round brackets, curved brackets, oval brackets, 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.

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", .^[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]).^[11]

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.)

Parentheses are included in the syntaxes of many computer 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.

Parentheses in mathematics signify a different precedence of operators. For example: $2 + 3 \times 4$ equals 14, since the multiplication is done before the addition. However, $(2 + 3) \times 4$ 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:

[(2+3)\times 4]^{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 also represent intervals; $(0, 5)$ , for example, is the interval between 0 and 5, not including 0 or 5.

Parentheses may also be used to represent a binomial coefficient, and in chemistry to denote a polyatomic ion.

Since 2014, antisemites have used triple parentheses around the names of people to denote them as Jewish.

Unpaired parenthesis

Lowercase latin letters used as indexes, rather than bullets or numbers, followed by unpaired parenthesis, are used in ordered lists especially in:

educational testing,
technical writing and diagrams,
market research, and
elections

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").^[13]

Square brackets

Usage in journalism

Square brackets—also called crotchets or simply brackets (US)—are mainly used to insert explanatory material or to mark where a 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 when 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.^[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 intervals, commutators, the floor function, the Lie bracket, the Iverson bracket, and matrices.

Brackets can also be used in chemistry to represent the concentration of a chemical substance or to denote distributed charge in a complex ion.

Brackets are used in many computer programming languages, especially those derived or inspired by the C language, to indicate array indexing operators. In this context, the opening bracket is often pronounced as "sub", indicating a subscript.

Other uses

In linguistics, phonetic transcriptions are generally enclosed within 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.

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

Angle brackets

Chevrons ⟨ ⟩, similar to the commonly used less-than (<) and greater-than symbol (>), 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,

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

The inner product of two vectors is commonly written as $\langle a,b\rangle$ , but the notation $(a,b)$ is also used.

In mathematical physics, especially quantum mechanics, it is common to write the inner product between elements as $\langle a|b\rangle$ , as a short version of $\langle a|\cdot |b\rangle$ , or $\langle a|{\hat {O}}|b\rangle$ , where ${\hat {O}}$ 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 /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]

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.

Single and double pairs of comparison operators (<<, >>) (meaning much smaller than and much greater than) are sometimes used instead of guillemets («, ») (used as quotation marks in many languages) when the proper characters are not available.

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.^[25]

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. See also non-English usage of quotation marks.

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

In East Asian punctuation, angle brackets are used as quotation marks.

Lenticular brackets

Some East Asian languages use lenticular brackets 【】, a combination of brackets and parentheses called 方頭括號 in Chinese and 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 ⌉ 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.^[27]

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.^[28]^[29] 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" (Swedish: piggparenteser) ⁅ and ⁆ are used in Swedish dictionaries.^[30]

Specific uses

Computing

The various bracket characters are frequently used in many computer 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 arrays.^[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.

Law

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.

When quoted material is in any way altered, the alterations are enclosed in brackets within the quotation. For example: Plaintiff asserts his cause is just, stating, "[m]y causes is [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.))

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^[33]

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)^[33]

U+003C

Less-than sign

< <

<HTML>

U+003E

Greater-than sign

> >

U+007B

Left curly bracket

{

{round, square, curly}

U+007D

Right curly bracket

}

Quotation
(Western texts)^[34]^[35]

U+00AB

Left-pointing double angle quotation mark

« French quote »

U+00BB

Right-pointing double angle quotation mark

U+2039

Single left-pointing angle quotation mark

‹

‹ $x$ ›

U+203A

Single right-pointing angle quotation mark

›

U+201C

Left double quotation mark

“

“English quote”

U+201D

Right double quotation mark

”

U+2018

Left single quotation mark

‘

‘English quote’

U+2019

Right single quotation mark

’

U+201A

Single low-9 quotation mark

‚ &sbquo;

‚German quote‘ or ‚Polish quote’

U+201E

Double low-9 quotation mark

„ &bdquo;

„German quote“ or „Polish quote”

Floor and ceiling functions^[27]

U+2308

Left ceiling

⌈

⌈ceiling⌉

U+2309

Right ceiling

⌉

U+230A

Left floor

⌊

⌊floor⌋

U+230B

Right floor

⌋

Quine corners^[27]

U+231C

Top left corner

⌜

⌜quasi-quotation⌝
⌜editorial notation⌝

U+231D

Top right corner

⌝

U+231E

Bottom left corner

⌞

⌞editorial notation⌟

U+231F

Bottom right corner

⌟

Technical/mathematical
(specialized)^[27]^[36]^[37]^[38]

U+207D

Superscript left parenthesis

⁽

X⁽²⁾

U+207E

Superscript right parenthesis

⁾

U+208D

Subscript left parenthesis

₍

X₍₂₎

U+208E

Subscript right parenthesis

₎

U+239B

Left parenthesis upper hook

⎛

⎛
⎜
⎝

large parentheses

⎞
⎟
⎠

U+239C

Left parenthesis extension

⎜

U+239D

Left parenthesis lower hook

⎝

U+239E

Right parenthesis upper hook

⎞

U+239F

Right parenthesis extension

⎟

U+23A0

Right parenthesis lower hook

⎠

U+23A1

Left square bracket upper corner

⎡

⎡
⎢
⎣

large square brackets

⎤
⎥
⎦

U+23A2

Left square bracket extension

⎢

U+23A3

Left square bracket lower corner

⎣

U+23A4

Right square bracket upper corner

⎤

U+23A5

Right square bracket extension

⎥

U+23A6

Right square bracket lower corner

⎦

U+23A7

Left curly bracket upper hook

⎧

⎧
⎨
⎩

large curly brackets

⎫
⎬
⎭

U+23A8

Left curly bracket middle piece

⎨

U+23A9

Left curly bracket lower hook

⎩

U+23AB

Right curly bracket upper hook

⎫

U+23AC

Right curly bracket middle piece

⎬

U+23AD

Right curly bracket lower hook

⎭

U+23AA

Curly bracket extension

⎪

U+23B0

Upper left or lower right curly bracket section

⎰

⎰ ⎱
⎱ ⎰

U+23B1

Upper right or lower left curly bracket section

⎱

U+23B4

Top square bracket

⎴

horizontal square brackets

⎵

U+23B5

Bottom square bracket

⎵

U+23B6

Bottom square bracket over top square bracket

⎶

⎴	⎴	⎴	⎴	⎴	⎴	⎴	⎴	⎴
t	e	r	m	i	n	a	l
⎶	⎶	⎶	⎶	⎶	⎶	⎶	⎶	⎶
e	m	u	l	a	t	i	o	n
⎵	⎵	⎵	⎵	⎵	⎵	⎵	⎵	⎵

U+23B8

Left vertical box line

⎸

⎸boxed text⎹

U+23B9

Right vertical box line

⎹

U+23DC

Top parenthesis

⏜

horizontal parentheses

⏝

U+23DD

Bottom parenthesis

⏝

U+23DE

Top curly bracket

⏞

horizontal curly brackets

⏟

U+23DF

Bottom curly bracket

⏟

U+23E0

Top tortoise shell bracket

⏠

tortoise shell brackets

⏡

U+23E1

Bottom tortoise shell bracket

⏡

U+27C5

Left s-shaped bag delimiter

⟅

⟅…⟆

U+27C6

Right s-shaped bag delimiter

⟆

U+27D3

Lower right corner with dot

⟓

⟓pullback…pushout⟔

U+27D4

Upper left corner with dot

⟔

U+27E6

Mathematical left white square bracket

⟦

⟦white square brackets⟧

U+27E7

Mathematical right white square bracket

⟧

U+27E8

Mathematical left angle bracket

⟨ &lang;^{[e 1]}

⟨ $a$ , $b$ ⟩

U+27E9

Mathematical right angle bracket

⟩ &rang;^{[e 1]}

U+27EA

Mathematical left double angle bracket

⟪

⟪ $A$ , $B$ ⟫

U+27EB

Mathematical right double angle bracket

⟫

U+27EC

Mathematical left white tortoise shell bracket

⟬

⟬white tortoise shell brackets⟭

U+27ED

Mathematical right white tortoise shell bracket

⟭

U+27EE

Mathematical left flattened parenthesis

⟮

⟮flattened parentheses⟯

U+27EF

Mathematical right flattened parenthesis

⟯

U+2983

Left white curly bracket

⦃

⦃white curly brackets⦄

U+2984

Right white curly bracket

⦄

U+2985

Left white parenthesis

⦅

⦅white/double parentheses⦆

U+2986

Right white parenthesis

⦆

U+2987

Z notation left image bracket

⦇

$R$ ⦇ $S$ ⦈

U+2988

Z notation right image bracket

⦈

U+2989

Z notation left binding bracket

⦉

$A$ ⦉ $B$ ⦊

U+298A

Z notation right binding bracket

⦊

U+298B

Left square bracket with underbar

⦋

⦋underlined square brackets⦌

U+298C

Right square bracket with underbar

⦌

U+298D

Left square bracket with tick in top corner

⦍

⦍ticked square brackets⦎

U+298E

Right square bracket with tick in bottom corner

⦎

U+298F

Left square bracket with tick in bottom corner

⦏

⦏ticked square brackets⦐

U+2990

Right square bracket with tick in top corner

⦐

U+2991

Left angle bracket with dot

⦑

⦑dotted angle brackets⦒

U+2992

Right angle bracket with dot

⦒

U+2993

Left arc less-than bracket

⦓

⦓inequality sign brackets⦔

U+2994

Right arc greater-than bracket

⦔

U+2995

Double left arc greater-than bracket

⦕

⦕inequality sign brackets⦖

U+2996

Double right arc less-than bracket

⦖

U+2997

Left black tortoise shell bracket

⦗

⦗black tortoise shell brackets⦘

U+2998

Right black tortoise shell bracket

⦘

U+29D8

Left wiggly fence

⧘

⧘…⧙

U+29D9

Right wiggly fence

⧙

U+29DA

Left double wiggly fence

⧚

⧚…⧛

U+29DB

Right double wiggly fence

⧛

U+29FC

Left-pointing curved angle bracket

⧼

⧼…⧽

U+29FD

Right-pointing curved angle bracket

⧽

Half brackets^[39]

U+2E22

Top left half bracket

⸢

⸢editorial notation⸣

U+2E23

Top right half bracket

⸣

U+2E24

Bottom left half bracket

⸤

⸤editorial notation⸥

U+2E25

Bottom right half bracket

⸥

Dingbats^[40]

U+2768

Medium left parenthesis ornament

❨

❨medium parenthesis ornament❩

U+2769

Medium right parenthesis ornament

❩

U+276A

Medium flattened left parenthesis ornament

❪

❪medium flattened parenthesis ornament❫

U+276B

Medium flattened right parenthesis ornament

❫

U+276C

Medium left-pointing angle bracket ornament

❬

❬medium angle bracket ornament❭

U+276D

Medium right-pointing angle bracket ornament

❭

U+2770

Heavy left-pointing angle bracket ornament

❰

❰heavy angle bracket ornament❱

U+2771

Heavy right-pointing angle bracket ornament

❱

U+276E

Heavy left-pointing angle quotation mark ornament

❮

❮heavy angle quotation ornament❯

U+276F

Heavy right-pointing angle quotation mark ornament

❯

U+2772

Light left tortoise shell bracket ornament

❲

❲light tortoise shell bracket ornament❳

U+2773

Light right tortoise shell bracket ornament

❳

U+2774

Medium left curly bracket ornament

❴

❴medium curly bracket ornament❵

U+2775

Medium right curly bracket ornament

❵

Arabic^[41]

U+FD3E

Ornate left parenthesis

﴾

﴿العربية﴾‎

U+FD3F

Ornate right parenthesis

﴿

N'Ko^[39]

U+2E1C

Left low paraphrase bracket

⸜

⸜ߒߞߏ⸝‎

U+2E1D

Right low paraphrase bracket

⸝

Ogham^[42]

U+169B

Ogham feather mark

᚛

᚛ᚑᚌᚐᚋ᚜

U+169C

Ogham reversed feather mark

᚜

Old Hungarian

U+2E42

Double low-reversed-9 quotation mark

⹂

Tibetan^[43]

U+0F3A

Tibetan mark gug rtags gyon

༺

༺དབུ་ཅན་༻

U+0F3B

Tibetan mark gug rtags gyas

༻

U+0F3C

Tibetan mark ang khang gyon

༼

༼༡༢༣༽

U+0F3D

Tibetan mark ang khang gyas

༽

New Testament editorial marks^[39]

U+2E02

Left substitution bracket

⸂

⸂…⸃

U+2E03

Right substitution bracket

⸃

U+2E04

Left dotted substitution bracket

⸄

⸄…⸅

U+2E05

Right dotted substitution bracket

⸅

U+2E09

Left transposition bracket

⸉

⸉…⸊

U+2E0A

Right transposition bracket

⸊

U+2E0C

Left raised omission bracket

⸌

⸌…⸍

U+2E0D

Right raised omission bracket

⸍

Medieval studies^[35]^[39]

U+2045

Left square bracket with quill

⁅

U+2046

Right square bracket with quill

⁆

U+2E26

Left sideways u bracket

⸦

⸦crux⸧

U+2E27

Right sideways u bracket

⸧

U+2E28

Left double parenthesis

⸨

⸨…⸩

U+2E29

Right double parenthesis

⸩

Quotation
(East-Asian texts)^[44]

U+3014

Left tortoise shell bracket

〔

〔…〕

U+3015

Right tortoise shell bracket

〕

U+3016

Left white lenticular bracket

〖

〖…〗

U+3017

Right white lenticular bracket

〗

U+3018

Left white tortoise shell bracket

〘

〘…〙

U+3019

Right white tortoise shell bracket

〙

U+301A

Left white square bracket

〚

〚…〛

U+301B

Right white square bracket

〛

U+301D

Reversed double prime quotation mark

〝

〝…〟

U+301F

Low double prime quotation mark

〟^{[e 2]}

Quotation
(halfwidth East-Asian texts)^[27]^[45]

U+2329

Left-pointing angle bracket

〈 &lang;^{[e 1]}

〈deprecated〉

U+232A

Right-pointing angle bracket

〉 &rang;^{[e 1]}

U+FF62

Halfwidth left corner bracket

｢

｢ｶﾀｶﾅ｣

U+FF63

Halfwidth right corner bracket

｣

Quotation
(fullwidth East-Asian texts)^[44]

U+3008

Left angle bracket

〈

〈한〉

U+3009

Right angle bracket

〉

U+300A

Left double angle bracket

《

《한》

U+300B

Right double angle bracket

》

U+300C

Left corner bracket

「

「白八櫨」

U+300D

Right corner bracket

」

U+300E

Left white corner bracket

『

『カタカナ』

U+300F

Right white corner bracket

』

U+3010

Left black lenticular bracket

【

【ひらがな】

U+3011

Right black lenticular bracket

】

General purpose
(fullwidth East-Asian)^[45]

U+FF08

Fullwidth left parenthesis

（

（Ｗｉｋｉ）

U+FF09

Fullwidth right parenthesis

）

U+FF3B

Fullwidth left square bracket

［

［ｓｉｃ］

U+FF3D

Fullwidth right square bracket

］

Technical/mathematical
(fullwidth East-Asian)^[45]

U+FF1C

Fullwidth less-than sign

＜

＜ＨＴＭＬ＞

U+FF1E

Fullwidth greater-than sign

＞

U+FF5B

Fullwidth left curly bracket

｛

｛１、２｝

U+FF5D

Fullwidth right curly bracket

｝

U+FF5F

Fullwidth left white parenthesis

｟

｟…｠

U+FF60

Fullwidth right white parenthesis

｠

1 2 3 4 &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.
↑ U+301F LOW DOUBLE PRIME QUOTATION MARK is preferred over U+301E DOUBLE PRIME QUOTATION MARK

Braces (curly brackets) first became part of a character set with the 8-bit code of the IBM 7030 Stretch.^[46]

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,^[27] 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 2 "Terminology Search - Microsoft". Microsoft Language Portal - Terminology Collection. Retrieved 21 November 2016.
↑ Truss, Lynne. Eats, Shoots & Leaves, 2003. p. 161. ISBN 1-59240-087-6.
↑ Smith, John. The printer’s grammar: containing a concise history of the origin of printing; Also, an examination of the superficies, gradation, and properties of The different sizes of types cast by letter founders; Various Tables of Calculation; Models of Letter Cases; Schemes for casting off Copy and Imposing; and many other Requisites for attaining a perfect Knowledge both in the Theory and Practice of the Art of Printing. With directions to authors, compilers, &c. How to Prepare Copy, and to Correct their own Proofs. Chiefly collected from SMITH’s edition. To which are added directions for pressmen, &c. The whole calculated for the Service of All who have any Concern in the Letter Press. p. 84.
↑ Concise Oxford Dictionary, 10th Edition, Oxford University Press, Great Clarendon Street, Oxford OX2 2DP, UK
↑ "broket". Catb.org. Retrieved 2013-02-13.
↑ Merriam-Webster's Manual for Writers and Editors. Merriam-Webster. 1998. p. 149. ISBN 0-87779-622-X. At Google Books.
↑ Robert Bringhurst, The Elements of Typographic Style, §5.3.2.
↑ Forsmann, Friedrich; DeJong, Ralf (2004). Detailtypografie [Detail Typography] (in German). Mainz: Herrmann Schmidt. p. 263. ISBN 978-3874396424.
↑ Straus, Jane. "Parentheses — Punctuation Rules". The Blue Book of Grammar and Punctuation. grammarbook.com. Retrieved 18 April 2014.
↑ Slash (punctuation)#Gender-neutrality in Spanish and Portuguese
↑ Fogarty, Mignon. "Parentheses, Brackets, and Braces". Quick and Dirty Tips. Retrieved 27 March 2011.
↑ http://math.about.com/od/mathhelpandtutorials/fl/Parenthesis-Braces-and-Brackets.html[]
↑ "The Free Online Dictionary". Thefreedictionary.com. Retrieved 2013-02-13.
↑ The Chicago Manual of Style, 15th ed., The University of Chicago Press, 2003, §6.104
↑ "Bartleby.com: Great Books Online -- Quotes, Poems, Novels, Classics and hundreds more". bartleby.com. Archived from the original on 24 May 2008.
↑ The Chicago Manual of Style, 15th ed., The University of Chicago Press, 2003, §6.102 and §6.106
↑ The Chicago Manual of Style, 15th ed., The University of Chicago Press, 2003, §6.105
↑ The Chicago Manual of Style, 15th ed., The University of Chicago Press, 2003, §6.107
↑ Decodeunicode.org > U+007B LEFT CURLY BRACKET Retrieved on 3 May 2009
↑ "Brace and Indent Styles and Code Convention". riedquat.de.
↑ K R Venugopa, Rajkumar Buyya, T Ravishankar. Mastering C++, 1999. p. 34. ISBN 0-07-463454-2.
↑ Bauer, Laurie (2007). "Notational conventions. Brackets". The Linguistics Student's Handbook. Edinburgh: Edinburgh University Press. p. 99.
1 2 Sampson, Geoffrey (2016). "Writing systems: methods for recording language". In Allan, Keith. The Routledge Handbook of Linguistics. Routledge. p. 60.
1 2 Trask, Robert Lawrence (2000). "Angle brackets". The Dictionary of Historical and Comparative Linguistics. Edinburgh: Edinburgh University Press. p. 22.
↑ "The Two Kinds Archive". 29 September 2004. Retrieved 2009-09-27.
↑ M.L. West (1973) Textual Criticism and Editorial Technique (Stuttgart) 81.
1 2 3 4 5 6 "Miscellaneous Technical Code Chart" (PDF), The Unicode Standard, retrieved 2016-02-27
↑ Dowty, D., Wall, R. and Peters, S.: 1981, Introduction to Montague semantics, Springer.
↑ Scott, D. and Strachey, C.: 1971, Toward a mathematical semantics for computer languages, Oxford University Computing Laboratory, Programming Research Group.
↑ See sv:Parentes
↑ Brian W. Kernaghan, Dennis M. Ritchie. "The C Programming Language", 1988. p. 7. ISBN 0-13-110370-9
↑ Bjarne Stroustrup, "The C++ Programming Language", 2013. p.39. ISBN 0-13-352285-7
1 2 "C0 Controls and Basic Latin Code Chart" (PDF), The Unicode Standard, retrieved 2016-02-27
↑ "C1 Controls and Latin-1 Supplement Code Chart" (PDF), The Unicode Standard, retrieved 2016-02-27
1 2 "General Punctuation Code Chart" (PDF), The Unicode Standard, retrieved 2016-03-01
↑ "Superscripts and Subscripts Code Chart" (PDF), The Unicode Standard, retrieved 2016-02-27
↑ "Miscellaneous Mathematical Symbols-A Code Chart" (PDF), The Unicode Standard, retrieved 2016-02-27
↑ "Miscellaneous Mathematical Symbols-B Code Chart" (PDF), The Unicode Standard, retrieved 2016-02-27
1 2 3 4 "Supplemental Punctuation Code Chart" (PDF), The Unicode Standard, retrieved 2016-02-27
↑ "Dingbats Code Chart" (PDF), The Unicode Standard, retrieved 2016-02-27
↑ "Arabic Presentation Forms-A Code Chart" (PDF), The Unicode Standard, retrieved 2016-02-27
↑ "Ogham Code Chart" (PDF), The Unicode Standard, retrieved 2016-02-27
↑ "Tibetan Code Chart" (PDF), The Unicode Standard, retrieved 2016-02-27
1 2 "CJK Symbols and Punctuation Code Chart" (PDF), The Unicode Standard, retrieved 2016-02-27
1 2 3 "Halfwidth and Fullwidth Forms Code Chart" (PDF), The Unicode Standard, retrieved 2016-02-27
↑ Bob, Bemer. "The Great Curly Brace Trace Chase". Retrieved 2009-09-05.

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

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