# Bracket

# Bracket

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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*,^{[3]} respectively, depending of the directionality of the context.

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 North America, an unqualified 'bracket' typically refers to the square bracket; in Britain, the round bracket.

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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.^{[4]}

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, or circle brackets

{ } – braces are "two connecting marks used in printing"; and in music "to connect staves to be performed at the same time"

^{[5]}(UK and US), 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, second brackets, fancy brackets, M Brace, moustache brackets.[ ] – square brackets, closed brackets, hard brackets, third brackets, crotchets,

^{[6]}or brackets (US)⟨ ⟩ – pointy brackets, angle brackets, triangular brackets, diamond brackets, tuples, or chevrons

< > – guillemets, 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".

^{[7]}⸤ ⸥; ｢ ｣ – corner brackets

⟦ ⟧ – double square brackets, white square brackets, Scott brackets

〔 〕 – tortoise shell brackets

*Guillemets*, ‹ › and « », are sometimes referred to as chevrons or [double] angle brackets, but are not used as brackets.^{[8]}

Typography

The characters ‹ › and « », known as *guillemets* or angular quote brackets, are actually quotation mark glyphs used in several European languages.^{[9]} Which one of each pair is the opening quote mark and which is the closing quote varies between languages.

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

In English, typographers mostly prefer not to set brackets in italics, even when the enclosed text is italic.^{[10]} However, in other languages like German, if brackets enclose text in italics, they are usually also set in italics.^{[11]}

Types and uses

Parentheses

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.^{[12]} 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).^{[13]}

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").^{[14]}

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:

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.^{[15]}

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 be used to represent a binomial coefficient.

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:^{[16]}

- 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

Usage online

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

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.^{[17]}

A bracketed ellipsis, […], is often used to indicate omitted material: "I'd like to thank [several unimportant people] for their tolerance [...]"^{[18]}
Bracketed comments inserted into a quote indicate where the original has been modified for clarity: "I appreciate it [the honor], but I must refuse", and "the future of psionics [see definition] is in doubt". Or one can quote the original statement "I hate to do laundry" with a (sometimes grammatical) modification inserted: He "hate[s] to do laundry".

Additionally, a small letter can be replaced by a capital one, when the beginning of the original text is omitted for succinctness, for example, when referring to a verbose original: "To the extent that policymakers and elite opinion in general have made use of economic analysis at all, they have, as the saying goes, done so the way a drunkard uses a lamppost: for support, not illumination", it can be quoted succinctly as: "[P]olicymakers […] made use of economic analysis […] the way a drunkard uses a lamppost: for support, not illumination." When nested parentheses are needed, brackets are used as a substitute for the inner pair of parentheses within the outer pair.^{[19]} 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.^{[20]}
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:

Usage in scientific fields

`Brackets are used inmathematicsin a variety of notations, including standard notations forcommutators, thefloor function, theLie bracket,equivalence classes, theIverson bracket, andmatrices. Square brackets may also represent closedintervals;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

In linguistics, phonetic transcriptions are generally enclosed within brackets,^{[21]} 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

**Curly brackets** { and }, also known as curly braces (UK and US), 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).^{[22]} 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.^{[23]}

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.^{[24]}. They are used for Enumerated type, eg in C. In syntax diagrams they are used for repetition eg in Extended Backus–Naur form.

Angle brackets

Chevrons ⟨ ⟩, similar to the commonly used less-than (<) and greater-than sign (>), are often used to enclose highlighted material.

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

The inner product of two vectors is commonly written as ⟨*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, chevrons indicate graphemes (i.e., written letters) or orthography, as in "The English word /kæt/ is spelled ⟨cat⟩."^{[25]}^{[26]}^{[27]}

In epigraphy, they may be used for mechanical transliterations of a text into the Latin script.^{[26]}

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.^{[27]}

In HTML, chevrons (greater and less than symbols) are used to bracket meta text. For example “**” denotes that the following text should be displayed as bold. Pairs of meta text tags are required - much as brackets themselves are usually in pairs. The end of the bold text segment would be indicated by “**”. This usage is sometimes extended as a mechanism for communicating mood, or tone, in digital formats such as messaging, for example adding “

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*) 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.

Lenticular brackets

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.^{[28]} For example, Callimachus *Iambus* 1.2 reads: ἐκ τῶν ὅκου βοῦν κολλύ⸤βου π⸥ιπρήσκουσιν. A hole in the papyrus has obliterated βου π, but these letters are supplied by an ancient commentary on the poem. Second intermittent sources can be between ⸢ and ⸣. Quine corners are sometimes used instead of half brackets.^{[29]}

Double brackets

Double brackets (or white square brackets), ⟦ ⟧, are used to indicate the *semantic evaluation function* in formal semantics for natural language and denotational semantics for programming languages.^{[30]}^{[31]} 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.

Brackets with quills

Known as "spike parentheses" (Swedish: *piggparenteser*) ⁅ and ⁆ are used in Swedish dictionaries.^{[32]}

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.^{[33]}^{[34]}

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. 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.))

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^{[35]} | 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) ^{[35]} | U+003C | Less-than sign | < < | |

U+003E | Greater-than sign | > > | ||

U+007B | Left curly bracket | { | {round, square, curly} | |

U+007D | Right curly bracket | } | ||

Quotation (Western texts) ^{[36]}^{[37]} | 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 | ‚ ‚ | ‚German quote‘ or ‚Polish quote’ | |

U+201E | Double low-9 quotation mark | „ „ | „German quote“ or „Polish quote” | |

Floor and ceiling functions^{[29]} | U+2308 | Left ceiling | ⌈ | ⌈ceiling⌉ |

U+2309 | Right ceiling | ⌉ | ||

U+230A | Left floor | ⌊ | ⌊floor⌋ | |

U+230B | Right floor | ⌋ | ||

Quine corners^{[29]} | 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) ^{[29]}^{[38]}^{[39]}^{[40]} | ||||

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 | ⎰ | ⎰ ⎱more curly brackets⎱ ⎰ | |

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 | ⎶ | ||

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 | ⟨ ⟨^{[1]} | ⟨*a*, *b*⟩ | |

U+27E9 | Mathematical right angle bracket | ⟩ ⟩^{[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 | ⦇ | ⦇S*⦈ | |

U+2988 | Z notation right image bracket | ⦈ | ||

U+2989 | Z notation left binding bracket | ⦉ | ⦉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+2990 | Right square bracket with tick in top corner | ⦐ | ||

U+298E | Right square bracket with tick in bottom corner | ⦎ | ⦏ticked square brackets⦎ | |

U+298F | Left square bracket with tick in bottom 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^{[41]} | 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^{[42]} | 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^{[43]} | U+FD3E | Ornate left parenthesis | ﴾ | ﴿العربية﴾ |

U+FD3F | Ornate right parenthesis | ﴿ | ||

N'Ko^{[41]} | U+2E1C | Left low paraphrase bracket | ⸜ | ⸜ߒߞߏ⸝ |

U+2E1D | Right low paraphrase bracket | ⸝ | ||

Ogham^{[44]} | U+169B | Ogham feather mark | ᚛ | ᚛ᚑᚌᚐᚋ᚜ |

U+169C | Ogham reversed feather mark | ᚜ | ||

Old Hungarian | U+2E42 | Double low-reversed-9 quotation mark | ⹂ | ⹂ |

Tibetan^{[45]} | 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^{[41]} | 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^{[37]}^{[41]} | 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) ^{[46]} | 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+301E | Double prime quotation mark | 〞^{[2]} | ||

Quotation (halfwidth East-Asian texts) ^{[29]}^{[47]} | U+2329 | Left-pointing angle bracket | 〈 ⟨^{[1]} | 〈deprecated〉 |

U+232A | Right-pointing angle bracket | 〉 ⟩^{[1]} | ||

U+FF62 | Halfwidth left corner bracket | ｢ | ｢ｶﾀｶﾅ｣ | |

U+FF63 | Halfwidth right corner bracket | ｣ | ||

Quotation (fullwidth East-Asian texts) ^{[46]} | 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 | 「 | 「表題」 | |

U+300D | Right corner bracket | 」 | ||

U+300E | Left white corner bracket | 『 | 『表題』 | |

U+300F | Right white corner bracket | 』 | ||

U+3010 | Left black lenticular bracket | 【 | 【表題】 | |

U+3011 | Right black lenticular bracket | 】 | ||

General purpose (fullwidth East-Asian) ^{[47]} | 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) ^{[47]} | 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 | ｠ |

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

The angle brackets or chevrons at U+27E8 and U+27E9 are for mathematical use and Western languages, whereas U+3008 and U+3009 are for East Asian languages. The chevrons at U+2329 and U+232A are deprecated in favour of the U+3008 and U+3009 East Asian angle brackets. Unicode discourages their use for mathematics and in Western texts,^{[29]} 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

*Unicode Technical Reports*. Retrieved 24 April 2018.

*Eats, Shoots & Leaves*, 2003. p. 161. ISBN 1-59240-087-6.

*Microsoft Language Portal - Terminology Collection*. Retrieved 21 November 2016.

*Merriam-Webster's Manual for Writers and Editors*. Merriam-Webster. 1998. p. 149. ISBN 0-87779-622-X – via Google Books.

*The Elements of Typographic Style*, §5.3.2.

*Detailtypografie*[

*Detail Typography*] (in German). Mainz: Herrmann Schmidt. p. 263. ISBN 978-3874396424.

*The Blue Book of Grammar and Punctuation*. grammarbook.com. Retrieved 18 April 2014.

*CODATA reference*. NIST. Retrieved 20 July 2018.

*The Chicago Manual of Style, 15th ed.*, The University of Chicago Press, 2003, §6.104

*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