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This article is about the family of punctuation marks. Bracket_sentence_0

For other uses, see Bracket (disambiguation). Bracket_sentence_1

"Parenthesis" and "Parenthetical" redirect here. Bracket_sentence_2

For other uses, see Parenthesis (disambiguation). Bracket_sentence_3

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. Bracket_sentence_4

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, respectively, depending on the directionality of the context. Bracket_sentence_5

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. Bracket_sentence_6

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. Bracket_sentence_7

In the United States, an unqualified 'bracket' typically refers to the square bracket; in Britain and most other English-speaking countries, the round bracket. Bracket_sentence_8

History Bracket_section_0

⟨ ⟩ were the earliest type of bracket to appear in written English. Bracket_sentence_9

Desiderius Erasmus coined the term lunula to refer to the rounded ( ) recalling the shape of the crescent moon (Latin: luna). Bracket_sentence_10

Names for various bracket symbols Bracket_section_1

Typography Bracket_section_2

In English, typographers mostly prefer not to set brackets in italics, even when the enclosed text is italic. Bracket_sentence_11

However, in other languages like German, if brackets enclose text in italics, they are usually also set in italics. Bracket_sentence_12

Types and uses Bracket_section_3

Parentheses Bracket_section_4

Various terms redirect here. Bracket_sentence_13

For other uses, see parenthesis (disambiguation), paren (disambiguation), parenthetical referencing, Parens (moth), ( ) (disambiguation), and Parenthetical Girls. Bracket_sentence_14

Due to technical restrictions, titles like :) redirect here. Bracket_sentence_15

For typographical portrayals of faces, see emoticon. Bracket_sentence_16

Uses in writing Bracket_section_5

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. Bracket_sentence_17

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. Bracket_sentence_18

That issue is fixed by using a pair of dashes instead, to the . Bracket_sentence_19

In American usage, parentheses are usually considered separate from other brackets, and calling them "brackets" is unusual. Bracket_sentence_20

Parentheses may be used in formal writing to add supplementary information, such as "Sen. John McCain (R - Arizona) spoke at length". Bracket_sentence_21

They can also indicate shorthand for "either singular or plural" for nouns, e.g. "the claim(s)". Bracket_sentence_22

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). Bracket_sentence_23

Parenthetical phrases have been used extensively in informal writing and stream of consciousness literature. Bracket_sentence_24

Examples include the southern American author William Faulkner (see Absalom, Absalom! Bracket_sentence_25

and the Quentin section of The Sound and the Fury) as well as poet E. Bracket_sentence_26 E. Cummings. Bracket_sentence_27

Parentheses have historically been used where the dash is currently used in alternatives, such as "parenthesis)(parentheses". Bracket_sentence_28

Examples of this usage can be seen in editions of Fowler's. Bracket_sentence_29

Parentheses may be nested (generally with one set (such as this) inside another set). Bracket_sentence_30

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]). Bracket_sentence_31

Any punctuation inside parentheses or other brackets is independent of the rest of the text: "Mrs. Pennyfarthing (What? Bracket_sentence_32

Yes, that was her name!) Bracket_sentence_33

was my landlady." Bracket_sentence_34

In this use, the explanatory text in the parentheses is a parenthesis. Bracket_sentence_35

Parenthesized text is usually short and within a single sentence. Bracket_sentence_36

Where several sentences of supplemental material are used in parentheses the final full stop would be within the parentheses, or simply omitted. Bracket_sentence_37

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. Bracket_sentence_38

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"). Bracket_sentence_39

Uses in enumerations Bracket_section_6

Lower-case Latin letters used as indexes, rather than bullets or numbers, followed by an unpaired parenthesis, are used in ordered especially in: a) educational testing, b) technical writing and diagrams, c) market research, and d) elections. Bracket_sentence_40

Uses in mathematics Bracket_section_7

Parentheses are used in mathematical notation to indicate grouping, often inducing a different order of operations. Bracket_sentence_41

For example: in the usual order of algebraic operations, 4 × 3 + 2 equals 14, since the multiplication is done before the addition. Bracket_sentence_42

However, 4 × (3 + 2) equals 20, because the parentheses override normal precedence, causing the addition to be done first. Bracket_sentence_43

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. Bracket_sentence_44

Example: Bracket_sentence_45

A related convention is that when parentheses have two levels of nesting, curly brackets (braces) are the outermost pair. Bracket_sentence_46

Following this convention, when more than three levels of nesting are needed, often a cycle of parentheses, square brackets, and curly brackets will continue. Bracket_sentence_47

This helps to distinguish between one such level and the next. Bracket_sentence_48

Parentheses are also used to set apart the arguments in mathematical functions. Bracket_sentence_49

For example, f(x) is the function f applied to the variable x. Bracket_sentence_50

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. Bracket_sentence_51

Parentheses may be used to represent a binomial coefficient, and also matrices. Bracket_sentence_52

Uses in programming languages Bracket_section_8

See also: Bracing style Bracket_sentence_53

Parentheses are included in the syntaxes of many programming languages. Bracket_sentence_54

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. Bracket_sentence_55

In some cases, such as in LISP, parentheses are a fundamental construct of the language. Bracket_sentence_56

They are also often used for scoping functions and for arrays. Bracket_sentence_57

In syntax diagrams they are used for grouping eg in Extended Backus–Naur form. Bracket_sentence_58

Uses in other scientific fields Bracket_section_9

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). Bracket_sentence_59

They can be used in various fields as notation to indicate the amount of uncertainty in a numerical quantity. Bracket_sentence_60

For example: Bracket_sentence_61


  • 1234.56789(11)Bracket_item_0_0

is equivalent to: Bracket_sentence_62


  • 1234.56789 ± 0.00011Bracket_item_1_1

e.g. the value of the Boltzmann constant could be quoted as 1.38064852(79)×10 J⋅K Bracket_sentence_63

Square brackets Bracket_section_10

Uses in published text Bracket_section_11

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. Bracket_sentence_64

In transcribed interviews, sounds, responses and reactions that are not words but that can be described are set off in square brackets — "... [laughs] ...". Bracket_sentence_65

A bracketed ellipsis, [...], is often used to indicate omitted material: "I'd like to thank [several unimportant people] for their tolerance [...]" 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". Bracket_sentence_66

Or one can quote the original statement "I hate to do laundry" with a (sometimes grammatical) modification inserted: He "hate[s] to do laundry". Bracket_sentence_67

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 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." Bracket_sentence_68

When nested parentheses are needed, brackets are sometimes used as a substitute for the inner pair of parentheses within the outer pair. Bracket_sentence_69

When deeper levels of nesting are needed, convention is to alternate between parentheses and brackets at each level. Bracket_sentence_70

Alternatively, empty square brackets can also indicate omitted material, usually single letter only. Bracket_sentence_71

The original, "Reading is also a process and it also changes you." Bracket_sentence_72

can be rewritten in a quote as: It has been suggested that reading can "also change[] you". Bracket_sentence_73

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. Bracket_sentence_74

In translated works, brackets are used to signify the same word or phrase in the original language to avoid ambiguity. Bracket_sentence_75

For example: He is trained in the way of the open hand [karate]. Bracket_sentence_76

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." Bracket_sentence_77

However, this guidance has little relevance outside of the technological constraints of the industry and era. Bracket_sentence_78

Uses in proofreading Bracket_section_12

Brackets (called move-left symbols or move right symbols) are added to the sides of text in proofreading to indicate changes in indentation: Bracket_sentence_79


Move leftBracket_header_cell_0_0_0 [To Fate I sue, of other means bereft, the only refuge for the wretched left.Bracket_cell_0_0_1
CenterBracket_header_cell_0_1_0 ]Paradise Lost[Bracket_cell_0_1_1
Move upBracket_header_cell_0_2_0 Bracket_cell_0_2_1

Uses in scientific fields Bracket_section_13

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. Bracket_sentence_80

Uses in programming languages Bracket_section_14

Brackets are used in many computer programming languages, primarily to force the order of evaluation and for parameter lists and array indexing. Bracket_sentence_81

But they are also used to denote general tuples, sets and other structures, just as in mathematics. Bracket_sentence_82

There may be several other uses as well, depending on the language at hand. Bracket_sentence_83

In syntax diagrams they are used for optional eg in Extended Backus–Naur form. Bracket_sentence_84

Uses in linguistics Bracket_section_15

See also: International Phonetic Alphabet § Brackets and transcription delimiters Bracket_sentence_85

In linguistics, phonetic transcriptions are generally enclosed within square brackets, often using the International Phonetic Alphabet, whereas phonemic transcriptions typically use paired slashes. Bracket_sentence_86

Pipes (| |) are often used to indicate a morphophonemic rather than phonemic representation. Bracket_sentence_87

Other conventions are double slashes (// //), double pipes (|| ||) and curly brackets ({ }). Bracket_sentence_88

In lexicography, square brackets usually surround the section of a dictionary entry which contains the etymology of the word the entry defines. Bracket_sentence_89

Other Bracket_section_16

Square brackets are used to denote parts of the text that need to be checked when preparing drafts prior to finalizing a document. Bracket_sentence_90

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. Bracket_sentence_91

Curly brackets Bracket_section_17

Curly brackets { and }, also known as curly braces (UK and US) or simply braces, flower brackets (India) and squiggly brackets (colloquially), are rarely used in prose and have no widely accepted use in formal writing, but may be used to mark words or sentences that should be taken as a group, to avoid confusion when other types of brackets are already in use, or for a special purpose specific to the publication (such as in a dictionary). Bracket_sentence_92

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. Bracket_sentence_93

In music, they are known as "accolades" or "braces", and connect two or more lines (staves) of music that are played simultaneously. Bracket_sentence_94

In mathematics they delimit sets and are often also used to denote the Poisson bracket between two quantities. Bracket_sentence_95

Uses in programming languages Bracket_section_18

See also: Bracing style Bracket_sentence_96

In many programming languages, curly brackets enclose groups of statements and create a local scope. Bracket_sentence_97

Such languages (C, C#, C++ and many others) are therefore called curly bracket languages. Bracket_sentence_98

They are used for enumerated type, eg in C. Bracket_sentence_99

In syntax diagrams they are used for repetition eg in Extended Backus–Naur form. Bracket_sentence_100

Phonetics Bracket_section_19

As an extension to the International Phonetic Alphabet, braces are used for prosodic notation. Bracket_sentence_101

Angle brackets Bracket_section_20

"Angle bracket" redirects here. Bracket_sentence_102

For a mechanical part used for joining, see Angle bracket (fastener). Bracket_sentence_103

Lenticular brackets Bracket_section_21

Some East Asian languages use lenticular brackets 【 】, a combination of square brackets and round brackets called (fāngtóu kuòhào) in Chinese and すみ付き (sumitsuki) in Japanese. Bracket_sentence_104

They are used for inference in Chinese and used in titles and headings in Japanese. Bracket_sentence_105

Floor and ceiling corners Bracket_section_22

The floor corner brackets ⌊ and ⌋, the ceiling corner brackets ⌈ and ⌉ (U+2308, U+2309) are used to denote the integer floor and ceiling functions. Bracket_sentence_106

Quine corners and half brackets Bracket_section_23

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. Bracket_sentence_107

Half brackets are used in English to mark added text, such as in translations: "Bill saw ⸤her⸥". Bracket_sentence_108

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. Bracket_sentence_109

For example, Callimachus Iambus 1.2 reads: ἐκ τῶν ὅκου βοῦν κολλύ⸤βου π⸥ιπρήσκουσιν. Bracket_sentence_110

A hole in the papyrus has obliterated βου π, but these letters are supplied by an ancient commentary on the poem. Bracket_sentence_111

Second intermittent sources can be between ⸢ and ⸣. Bracket_sentence_112

Quine corners are sometimes used instead of half brackets. Bracket_sentence_113

Double brackets Bracket_section_24

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. Bracket_sentence_114

The brackets stand for a function that maps a linguistic expression to its “denotation” or semantic value. Bracket_sentence_115

In mathematics, double brackets may also be used to denote intervals of integers or, less often, the floor function. Bracket_sentence_116

In papyrology, following the Leiden Conventions, they are used to enclose text that has been deleted in antiquity. Bracket_sentence_117

Brackets with quills Bracket_section_25

Known as "spike parentheses" (Swedish: piggparenteser), ⁅ and ⁆, are used in Swedish bilingual dictionaries to enclose supplemental constructions. Bracket_sentence_118

Specific uses Bracket_section_26

Computing Bracket_section_27

The various bracket characters are frequently used in many programming languages as operators or for other syntax markup. Bracket_sentence_119

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 ). Bracket_sentence_120

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. Bracket_sentence_121

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. Bracket_sentence_122

Mathematics Bracket_section_28

Main article: Bracket (mathematics) Bracket_sentence_123

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. Bracket_sentence_124

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. Bracket_sentence_125

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. Bracket_sentence_126

In some European countries, the notation [5, 12[ is also used for this. Bracket_sentence_127

The endpoint adjoining the bracket is known as closed, whereas the endpoint adjoining the parenthesis is known as open. Bracket_sentence_128

If both types of brackets are the same, the entire interval may be referred to as closed or open as appropriate. Bracket_sentence_129

Whenever +∞ or −∞ is used as an endpoint, it is normally considered open and adjoined to a parenthesis. Bracket_sentence_130

See Interval (mathematics) for a more complete treatment. Bracket_sentence_131

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⟩. Bracket_sentence_132

Mathematicians will also commonly write ⟨a, b⟩ for the inner product of two vectors. Bracket_sentence_133

In statistical mechanics, chevrons denote ensemble or time average. Bracket_sentence_134

Chevrons are used in group theory to write group presentations, and to denote the subgroup generated by a collection of elements. Bracket_sentence_135

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. Bracket_sentence_136

In group theory and ring theory, brackets denote the commutator. Bracket_sentence_137

In group theory, the commutator [g, h] is commonly defined as g h g h . Bracket_sentence_138

In ring theory, the commutator [a, b] is defined as a b − b a . Bracket_sentence_139

Furthermore, in ring theory, braces denote the anticommutator where {a, b} is defined as a b + b a . Bracket_sentence_140

The bracket is also used to denote the Lie derivative, or more generally the Lie bracket in any Lie algebra. Bracket_sentence_141

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. Bracket_sentence_142

In the Z formal specification language, braces define a set and chevrons define a sequence. Bracket_sentence_143

Accounting Bracket_section_29

Traditionally in accounting, contra amounts are placed in parentheses. Bracket_sentence_144

A debit balance account in a series of credit balances will have brackets and vice versa. Bracket_sentence_145

Credits to the contents of this page go to the authors of the corresponding Wikipedia page: