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  2. Numeric precision in Microsoft Excel - Wikipedia

    en.wikipedia.org/wiki/Numeric_precision_in...

    Excel does some rounding and / or 'snap to zero' for most of its results, in average chopping the last 3 bits of the IEEE double representation. This behavior can be switched of by setting the formula in parentheses: = ( 1 + 2^-52 - 1 ). You will see that even that small value survives.

  3. Propositional formula - Wikipedia

    en.wikipedia.org/wiki/Propositional_formula

    Starting after the second symbol, match the shortest subexpression y of x that has balanced parentheses. If x is a formula, there is exactly one symbol left after this expression, this symbol is a closing parenthesis, and y itself is a formula. This idea can be used to generate a recursive descent parser for formulas. Example of parenthesis ...

  4. Associative property - Wikipedia

    en.wikipedia.org/wiki/Associative_property

    In general, parentheses must be used to indicate the order of evaluation if a non-associative operation appears more than once in an expression (unless the notation specifies the order in another way, like /).

  5. Pumping lemma for regular languages - Wikipedia

    en.wikipedia.org/wiki/Pumping_lemma_for_regular...

    The proof that the language of balanced (i.e., properly nested) parentheses is not regular follows the same idea. Given p {\displaystyle p} , there is a string of balanced parentheses that begins with more than p {\displaystyle p} left parentheses, so that y {\displaystyle y} will consist entirely of left parentheses.

  6. Bracket (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Bracket_(mathematics)

    With some standard function when there is little chance of ambiguity, it is common to omit the parentheses around the argument altogether (e.g., ⁡). Note that this is never done with a general function f {\displaystyle f} , in which case the parenthesis are always included

  7. Dyck language - Wikipedia

    en.wikipedia.org/wiki/Dyck_language

    The number of distinct Dyck words with exactly n pairs of parentheses is the n-th Catalan number. Notice that the Dyck language of words with n parentheses pairs is equal to the union, over all possible k, of the Dyck languages of words of n parentheses pairs with k innermost pairs, as defined in

  8. Order of operations - Wikipedia

    en.wikipedia.org/wiki/Order_of_operations

    However, this convention is not universally understood, and some authors prefer explicit parentheses. [b] Some calculators and programming languages require parentheses around function inputs, some do not. Symbols of grouping can be used to override the usual order of operations. [2] Grouped symbols can be treated as a single expression. [2]

  9. Expression (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Expression_(mathematics)

    For a given combination of values for the free variables, an expression may be evaluated, although for some combinations of values of the free variables, the value of the expression may be undefined. Thus an expression represents an operation over constants and free variables and whose output is the resulting value of the expression. [22]