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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.
In mathematics, particularly in algebra, an indeterminate equation is an equation for which there is more than one solution. [1] For example, the equation a x + b y = c {\displaystyle ax+by=c} is a simple indeterminate equation, as is x 2 = 1 {\displaystyle x^{2}=1} .
When the function is of only one variable, it is of the form = +, where a and b are constants, often real numbers. The graph of such a function of one variable is a nonvertical line. a is frequently referred to as the slope of the line, and b as the intercept. If a > 0 then the gradient is positive and the graph slopes upwards
The above formula shows that its Lie algebra is the special linear Lie algebra consisting of those matrices having trace zero. Writing a 3 × 3 {\displaystyle 3\times 3} -matrix as A = [ a b c ] {\displaystyle A={\begin{bmatrix}a&b&c\end{bmatrix}}} where a , b , c {\displaystyle a,b,c} are column vectors of length 3, then the gradient over one ...
Indeterminate form is a mathematical expression that can obtain any value depending on circumstances. In calculus , it is usually possible to compute the limit of the sum, difference, product, quotient or power of two functions by taking the corresponding combination of the separate limits of each respective function.
If the slope is =, this is a constant function = defining a horizontal line, which some authors exclude from the class of linear functions. [3] With this definition, the degree of a linear polynomial would be exactly one, and its graph would be a line that is neither vertical nor horizontal.
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 ...
In this case, it is a partial function, and the set of real numbers on which the formula can be evaluated to a real number is called the natural domain or domain of definition of f. In many contexts, a partial function is called simply a function, and its natural domain is called simply its domain.