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).
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, respectively, depending on 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 the United States, an unqualified 'bracket' typically refers to the square bracket; in Britain and most other English-speaking countries, the round bracket.
History
⟨ ⟩ were the earliest type of bracket to appear in written English.
Desiderius Erasmus coined the term lunula to refer to the rounded ( ) recalling the shape of the crescent moon (Latin: luna).
Names for various bracket symbols
Typography
In English, typographers mostly prefer not to set brackets in italics, even when the enclosed text is italic.
However, in other languages like German, if brackets enclose text in italics, they are usually also set in italics.
Types and uses
Parentheses
Various terms redirect here.
For other uses, see parenthesis (disambiguation), paren (disambiguation), parenthetical referencing, Parens (moth), ( ) (disambiguation), and Parenthetical Girls.
Due to technical restrictions, titles like :) redirect here.
For typographical portrayals of faces, see emoticon.
Uses 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.
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 the .
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).
Parenthetical phrases have been used extensively in informal writing and stream of consciousness literature.
Examples include the southern American author William Faulkner (see Absalom, Absalom!
and the Quentin section of The Sound and the Fury) as well as poet E. E. Cummings.
Parentheses have historically been used where the dash is currently used in alternatives, such as "parenthesis)(parentheses".
Examples of this usage can be seen in editions of Fowler's.
Parentheses may be nested (generally with one set (such as this) inside another set).
This is not commonly used in formal writing (though sometimes other brackets [especially square brackets] will be used for one or more inner set of parentheses [in other words, secondary {or even tertiary} phrases can be found within the main parenthetical sentence]).
Any punctuation inside parentheses or other brackets is independent of the rest of the text: "Mrs. Pennyfarthing (What?
Yes, that was her name!)
was my landlady."
In this use, the explanatory text in the parentheses is a parenthesis.
Parenthesized text is usually short and within a single sentence.
Where several sentences of supplemental material are used in parentheses the final full stop would be within the parentheses, or simply omitted.
Again, the parenthesis implies that the meaning and flow of the text is supplemental to the rest of the text and the whole would be unchanged were the parenthesized sentences removed.
In more formal usage, "parenthesis" may refer to the entire bracketed text, not just to the punctuation marks used (so all the text in this set of round brackets may be said to be "a parenthesis", "a parenthetical", or "a parenthetical phrase").
Uses in enumerations
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.
Uses 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.
Parentheses are also used to set apart the arguments in mathematical functions.
For example, f(x) is the function f applied to the variable x.
In coordinate systems parentheses are used to denote a set of coordinates; so in the Cartesian coordinate system (4, 7) may represent the point located at 4 on the x-axis and 7 on the y-axis.
Parentheses may be used to represent a binomial coefficient, and also matrices.
Uses in programming languages
See also: Bracing style
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.
Uses 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:
- 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 J⋅K
Square brackets
Uses 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.
In transcribed interviews, sounds, responses and reactions that are not words but that can be described are set off in square brackets — "... [laughs] ...".
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".
Or one can quote the original statement "I hate to do laundry" with a (sometimes grammatical) modification inserted: He "hate[s] to do laundry".
Additionally, a small letter can be replaced by a capital one, when the beginning of the original printed text is being quoted in another piece of text or when the original text has been omitted for succinctness— for example, when referring to a original: "To the extent that policymakers and elite opinion in general have made use of economic analysis at all, they have, as the saying goes, done so the way a drunkard uses a lamppost: for support, not illumination", can be quoted succinctly as: "[P]olicymakers [...] have made use of economic analysis [...] the way a drunkard uses a lamppost: for support, not illumination."
When nested parentheses are needed, brackets are sometimes used as a substitute for the inner pair of parentheses within the outer pair.
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.
For example: He is trained in the way of the open hand [karate].
Style and usage guides originating in the news industry of the twentieth century, such as the AP Stylebook, recommend against the use of square brackets because "They cannot be transmitted over news wires."
However, this guidance has little relevance outside of the technological constraints of the industry and era.
Uses 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 |
Uses in scientific fields
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.
Uses 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.
Uses in linguistics
See also: International Phonetic Alphabet § Brackets and transcription delimiters
In linguistics, phonetic transcriptions are generally enclosed within square brackets, 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.
Other
Square brackets are used to denote parts of the text that need to be checked when preparing drafts prior to finalizing a document.
They often denote points that have not yet been agreed to in legal drafts and the year in which a report was made for certain case law decisions.
Curly brackets
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).
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.
In mathematics they delimit sets and are often also used to denote the Poisson bracket between two quantities.
Uses in programming languages
See also: Bracing style
In many programming languages, curly brackets enclose groups of statements and create a local scope.
Such languages (C, C#, C++ and many others) are therefore called curly bracket languages.
They are used for enumerated type, eg in C.
In syntax diagrams they are used for repetition eg in Extended Backus–Naur form.
Phonetics
As an extension to the International Phonetic Alphabet, braces are used for prosodic notation.
Angle brackets
"Angle bracket" redirects here.
For a mechanical part used for joining, see Angle bracket (fastener).
Lenticular brackets
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.
They are used for inference in Chinese and used in titles and headings in Japanese.
Floor and ceiling corners
The floor corner brackets ⌊ and ⌋, the ceiling corner brackets ⌈ and ⌉ (U+2308, U+2309) are used to denote the integer floor and ceiling functions.
Quine corners and half brackets
The Quine corners ⌜ and ⌝ have at least two uses in mathematical logic: either as quasi-quotation, a generalization of quotation marks, or to denote the Gödel number of the enclosed expression.
Half brackets are used in English to mark added text, such as in translations: "Bill saw ⸤her⸥".
In editions of papyrological texts, half brackets, ⸤ and ⸥ or ⸢ and ⸣, enclose text which is lacking in the papyrus due to damage, but can be restored by virtue of another source, such as an ancient quotation of the text transmitted by the papyrus.
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.
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.
The brackets stand for a function that maps a linguistic expression to its “denotation” or semantic value.
In mathematics, double brackets may also be used to denote intervals of integers or, less often, the floor function.
In papyrology, following the Leiden Conventions, they are used to enclose text that has been deleted in antiquity.
Brackets with quills
Known as "spike parentheses" (Swedish: piggparenteser), ⁅ and ⁆, are used in Swedish bilingual dictionaries to enclose supplemental constructions.
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.
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 h 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.
Credits to the contents of this page go to the authors of the corresponding Wikipedia page: en.wikipedia.org/wiki/Bracket.