and are
square brackets in both British and American English, but are also more simply
brackets in the latter. An older name for these brackets is "crotchets".
Uses of [ ] Square brackets are often used to insert explanatory material or to mark where a [word or] passage was omitted from an original material by someone other than the original author, or to mark modifications in quotations. In transcribed interviews, sounds, responses and reactions that are not words but that can be described are set off in square brackets—"... [laughs] ...". When quoted material is in any way altered, the alterations are enclosed in square brackets within the quotation to show that the quotation is not exactly as given, or to add an
annotation. For example:
The Plaintiff asserted his cause is just, stating, In the original quoted sentence, the word "my" was capitalised: it has been modified in the quotation given and the change signalled with brackets. Similarly, where the quotation contained a grammatical error (is/are), the quoting author signalled that the error was in the original with "[
sic]" (Latin for 'thus'). A bracketed
ellipsis, [...], is often used to indicate omitted material: "I'd like to thank [several unimportant people] for their tolerance [...]" Bracketed comments inserted into a quote indicate where the original has been modified for clarity: "I appreciate it [the honor], but I must refuse", and "the future of psionics [see definition] is in doubt". Or one can quote the original statement "I hate to do laundry" with a (sometimes grammatical) modification inserted: He "hate[s] to do laundry". Additionally, a small letter can be replaced by a capital one, when the beginning of the original printed text is being quoted in another piece of text or when the original text has been omitted for succinctness— for example, when referring to a
verbose original: "To the extent that policymakers and elite opinion in general have made use of economic analysis at all, they have, as the saying goes, done so the way a drunkard uses a lamppost: for support, not illumination", can be quoted succinctly as: "[P]olicymakers [...] have made use of economic analysis [...] the way a drunkard uses a lamppost: for support, not illumination." When nested parentheses are needed, brackets are sometimes used as a substitute for the inner pair of parentheses within the outer pair. 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". 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. In linguistics,
phonetic transcriptions are generally enclosed within square brackets, whereas
phonemic transcriptions typically use paired
slashes, according to
International Phonetic Alphabet rules. 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.
Proofreading Brackets (called
move-left symbols or
move right symbols) are added to the sides of text in
proofreading to indicate changes in indentation: Square brackets are used to denote parts of the text that need to be checked when preparing drafts prior to finalising a document.
Law Square brackets are used in some countries in the citation of
law reports to identify parallel citations to non-official reporters. For example: 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: This case is in the 1954 volume of the Appeal Cases reports, although the decision may have been given in 1953 or earlier. Compare with: This citation reports a decision from 1954, in volume 98 of the
Solicitors Journal which may have been published in 1955 or later. They often denote points that have not yet been agreed to in legal drafts and the year in which a report was made for certain
case law decisions.
Square brackets in mathematics Brackets are used in
mathematics in a variety of notations, including standard notations for
commutators, the
floor function, the
Lie bracket,
equivalence classes, the
Iverson bracket, and
matrices. Square brackets may be used exclusively or in combination with parentheses to represent
intervals as
interval notation. For example, represents the set of real numbers from 0 to 5 inclusive. Both parentheses and brackets are used to denote a
half-open interval; would be the set of all real numbers between 5 and 12, including 5 but not 12. The numbers may come as close as they like to 12, including 11.999 and so forth, but 12.0 is not included. In some European countries, the notation is also used. The endpoint adjoining the square bracket is known as
closed, whereas the endpoint adjoining the parenthesis is known as
open. In
group theory and
ring theory, brackets denote the
commutator. In group theory, the commutator is commonly defined as . In ring theory, the commutator is defined as .
Chemistry Square brackets can also be used in
chemistry to represent the
concentration of a
chemical substance in solution and to denote charge a Lewis structure of an ion (particularly distributed charge in a
complex ion), repeating chemical units (particularly in polymers) and transition state structures, among other uses.
Square brackets in programming languages Brackets are used in many computer
programming languages, primarily for
array indexing. But they are also used to denote general tuples, sets and other structures, just as in mathematics. There may be several other uses as well, depending on the language at hand. In
syntax diagrams they are used for optional portions, such as in
extended Backus–Naur form.
Double brackets ⟦ ⟧ Double brackets (or white square brackets or Scott brackets (named after
Dana Scott)), , are used to indicate the
semantic evaluation function in
formal semantics for natural language and
denotational semantics for programming languages. In the
Wolfram Language, double brackets, either as iterated single brackets () or ligatures (〚) are used for
list indexing. 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.
Lenticular brackets【】 Some
East Asian languages use lenticular brackets , a combination of square brackets and round brackets. In
Chinese, they are called () and in
Japanese, (). They are used in titles and headings in both Chinese and Japanese. On the Internet, they are used to emphasise a text. In Japanese, they are most frequently seen in dictionaries for quoting Chinese characters and Sino-Japanese loanwords.
Floor ⌊ ⌋ and ceiling ⌈ ⌉ corner brackets The floor corner brackets and ceiling corner brackets are used to denote the integer
floor and ceiling functions in mathematics.
Quine corners ⌜⌝ and half brackets ⸤ ⸥ or ⸢ ⸣ The Quine corners and have at least two uses in
mathematical logic: either as
quasi-quotation, a generalisation 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: "". A hole in the papyrus has obliterated "", 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. ==Curly brackets==