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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.
[3] [4] Likewise, for a function of several real variables, a critical point is a value in its domain where the gradient norm is equal to zero (or undefined). [ 5 ] This sort of definition extends to differentiable maps between R m {\displaystyle \mathbb {R} ^{m}} and R n , {\displaystyle \mathbb {R} ^{n},} a critical point ...
Unlike with functions, notational ambiguities can be overcome by means of additional definitions (e.g., rules of precedence, associativity of the operator). For example, in the programming language C , the operator - for subtraction is left-to-right-associative , which means that a-b-c is defined as (a-b)-c , and the operator = for assignment ...
A partial function from X to Y is thus a ordinary function that has as its domain a subset of X called the domain of definition of the function. If the domain of definition equals X, one often says that the partial function is a total function. In several areas of mathematics the term "function" refers to partial functions rather than to ...
The strict definition of an undefined value is a superficially valid (non-null) output which is meaningless but does not trigger undefined behaviour. For example, passing a negative number to the fast inverse square root function will produce a number.
This is an accepted version of this page This is the latest accepted revision, reviewed on 9 January 2025. 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 value, a condition where an expression does not have a ...
Can we imagine ourselves back on that awful day in the summer of 2010, in the hot firefight that went on for nine hours? Men frenzied with exhaustion and reckless exuberance, eyes and throats burning from dust and smoke, in a battle that erupted after Taliban insurgents castrated a young boy in the village, knowing his family would summon nearby Marines for help and the Marines would come ...
The function is a continuous ... but this definition can not be the same as the definition at other points. ... Defined and undefined; Degeneracy (mathematics ...