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In elementary algebra, parentheses ( ) are used to specify the order of operations. [1] Terms inside the bracket are evaluated first; hence 2×(3 + 4) is 14, 20 ÷ (5(1 + 1)) is 2 and (2×3) + 4 is 10. This notation is extended to cover more general algebra involving variables: for example (x + y) × (x − y). Square brackets are also often ...
Parentheses can be nested, and should be evaluated from the inside outward. For legibility, outer parentheses can be made larger than inner parentheses. Alternately, other grouping symbols, such as curly braces { } or square brackets [ ], are sometimes used along with parentheses ( ). For example:
Parentheses have historically been used where the em dash is currently used in alternatives, such as "parenthesis)(parentheses". Examples of this usage can be seen in editions of Fowler's Dictionary of Modern English Usage. Parentheses may be nested (generally with one set (such as this) inside another set).
For example, in the expression 3(x+y) the parentheses are symbols of grouping, but in the expression (3, 5) the parentheses may indicate an open interval. The most common symbols of grouping are the parentheses and the square brackets, and the latter are usually used to avoid too many repeated parentheses.
In standard truth-functional propositional logic, association, [4] [5] or associativity [6] are two valid rules of replacement. The rules allow one to move parentheses in logical expressions in logical proofs. The rules (using logical connectives notation) are: (()) (())
In logic, a set of symbols is commonly used to express logical representation. The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics.
An asterisk before a parenthesis indicates that the lack of the word or phrase inside is ungrammatical, while an asterisk after the opening bracket of the parenthesis indicates that the existence of the word or phrase inside is ungrammatical—e.g., the following indicates "go the station" would be ungrammatical: go *(to) the station
This section applies to both round brackets ( ), often called parentheses, and square brackets [ ]. If a sentence contains a bracketed phrase, place the sentence punctuation outside the brackets (as shown here). However, where one or more sentences are wholly inside brackets, place their punctuation inside the brackets.