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[1] Attempting to assign or use an undefined value within a particular formal system, may produce contradictory or meaningless results within that system. In practice, mathematicians may use the term undefined to warn that a particular calculation or property can produce mathematically inconsistent results, and therefore, it should be avoided. [2]
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} .
For a system of linear equations, the number of equations in an indeterminate system could be the same as the number of unknowns, less than the number of unknowns (an underdetermined system), or greater than the number of unknowns (an overdetermined system). Conversely, any of those three cases may or may not be indeterminate.
Given the two red points, the blue line is the linear interpolant between the points, and the value y at x may be found by linear interpolation.. In mathematics, linear interpolation is a method of curve fitting using linear polynomials to construct new data points within the range of a discrete set of known data points.
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.
It is inconsistent if and only if 0 = 1 is a linear combination (with polynomial coefficients) of the equations (this is Hilbert's Nullstellensatz). If an underdetermined system of t equations in n variables ( t < n ) has solutions, then the set of all complex solutions is an algebraic set of dimension at least n - t .
Slope illustrated for y = (3/2)x − 1.Click on to enlarge Slope of a line in coordinates system, from f(x) = −12x + 2 to f(x) = 12x + 2. The slope of a line in the plane containing the x and y axes is generally represented by the letter m, [5] and is defined as the change in the y coordinate divided by the corresponding change in the x coordinate, between two distinct points on the line.
[1] [2] [better source needed] In analysis , a mathematical expression such as 3 x 2 + 4 x {\displaystyle 3x^{2}+4x} is usually taken to represent a quantity whose value is a function of its variable x {\displaystyle x} , and the variable itself is taken to represent an unknown or changing quantity.
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