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In mathematics, the term undefined refers to a value, function, or other expression that cannot be assigned a meaning within a specific formal system. [ 1 ] Attempting to assign or use an undefined value within a particular formal system, may produce contradictory or meaningless results within that system.
Corner quotes, also called “Quine quotes”; for quasi-quotation, i.e. quoting specific context of unspecified (“variable”) expressions; [3] also used for denoting Gödel number; [4] for example “āGā” denotes the Gödel number of G. (Typographical note: although the quotes appears as a “pair” in unicode (231C and 231D), they ...
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]
This is an accepted version of this page This is the latest accepted revision, reviewed on 9 January 2025. Look up undefined in Wiktionary, the free dictionary. Undefined may refer to: Mathematics Undefined (mathematics), with several related meanings Indeterminate form, in calculus Computing Undefined behavior, computer code whose behavior is not specified under certain conditions Undefined ...
However it is not appropriate to call an expression "indeterminate form" if the expression is made outside the context of determining limits. An example is the expression 0 0 {\displaystyle 0^{0}} . Whether this expression is left undefined, or is defined to equal 1 {\displaystyle 1} , depends on the field of application and may vary between ...
This equation has two distinct solutions, x = 1 and x = 4, so the expression is undefined. In field theory, the expression a b {\textstyle {\frac {a}{b}}} is only shorthand for the formal expression ab −1 , where b −1 is the multiplicative inverse of b .
[1] pp.142--143 Since the same variable symbol may appear in multiple places in an expression, some occurrences of the variable symbol may be free while others are bound, [1] p.78 hence "free" and "bound" are at first defined for occurrences and then generalized over all occurrences of said variable symbol in the expression. However it is done ...
In languages where increment/decrement is not an expression (e.g., Go), only one version is needed (in the case of Go, post operators only). Since the increment/decrement operator modifies its operand, use of such an operand more than once within the same expression can produce undefined results.