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Sometimes, for the clarity of reading, different kinds of brackets are used to express the same meaning of precedence in a single expression with deep nesting of sub-expressions. [1] Historically, other notations, such as the vinculum, were similarly used for grouping. In present-day use, these notations all have specific meanings.
This means that to evaluate an expression, one first evaluates any sub-expression inside parentheses, working inside to outside if there is more than one set. Whether inside parenthesis or not, the operation that is higher in the above list should be applied first. Operations of the same precedence are conventionally evaluated from left to right.
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.
If the product operation is associative, the generalized associative law says that all these expressions will yield the same result. So unless the expression with omitted parentheses already has a different meaning (see below), the parentheses can be considered unnecessary and "the" product can be written unambiguously as
A formal expression is a kind of string of symbols, created by the same production rules as standard expressions, however, they are used without regard to the meaning of the expression. In this way, two formal expressions are considered equal only if they are syntactically equal, that is, if they are the exact same expression.
the first operation to be acted upon is any and all expressions found inside a parenthesis. So beginning at the left and moving to the right, find the first (and in this case, the only) parenthesis, that is, (2 + 2 2). Within the parenthesis itself is found the expression 2 2. The reader is required to find the value of 2 2 before going any ...
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9.3 Tall parentheses and fractions. 9.4 Integrals. 9.5 Matrices and determinants. 9.6 Summation. ... Breaking up a long expression so that it wraps when necessary ...
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