Square brackets [ ] 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.[10] A bracketed ellipsis […] is often used to indicate omitted material: "I'd like to thank [several unimportant people] for their tolerance..."[11] 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 modification inserted in the middle of it: 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.[12] 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.[13] For example: He is trained in the way of the open hand [karate]. In linguistics, phonetic transcriptions are generally enclosed within brackets,[14] 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 (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 Quote to be Moved Up.svg 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. 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. Curly brackets or braces { } Curly brackets – also called braces or (colloquially) squiggly brackets in the US – are used in specialized ways in poetry and music (to mark repeats or joined lines). The musical terms for this mark joining staves are accolade and "brace", and connect two or more lines of music that are played simultaneously.[15] In mathematics they delimit sets, and in writing, they may be used similarly, "Select your animal {goat, sheep, cow, horse} and follow me". In many programming languages, they enclose groups of statements. Such languages (C being one of the best-known examples) are therefore called curly bracket languages. Some people use a brace to signify movement in a particular direction.[citation needed][clarification needed] Presumably, due to the similarity of the words brace and bracket (although they do not share an etymology), many people mistakenly treat brace as a synonym for bracket. Therefore, when it is necessary to avoid any possibility of confusion, such as in computer programming, it may be best to use the term curly bracket rather than brace. However, general usage in North American English favours the latter form.[citation needed] Indian programmers often use the name "flower bracket".[16] In classical mechanics, curly brackets are often also used to denote the Poisson bracket between two quantities.