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In arithmetic, and therefore algebra, division by zero is undefined. [7] Use of a division by zero in an arithmetical calculation or proof, can produce absurd or meaningless results. Assuming that division by zero exists, can produce inconsistent logical results, such as the following fallacious "proof" that one is equal to two [ 8 ] :
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} .
The meaning of the expression should be the solution x of the equation =. But in the ring Z/6Z, 2 is a zero divisor. This equation has two distinct solutions, x = 1 and x = 4, so the expression is undefined.
[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.
Vertical line of equation x = a Horizontal line of equation y = b. Each solution (x, y) of a linear equation + + = may be viewed as the Cartesian coordinates of a point in the Euclidean plane. With this interpretation, all solutions of the equation form a line, provided that a and b are not both zero. Conversely, every line is the set of all ...
For example, the equation y 2 − x 3 = 0 defines a curve that has a cusp at the origin x = y = 0. One could define the x-axis as a tangent at this point, but this definition can not be the same as the definition at other points. In fact, in this case, the x-axis is a "double tangent."
In mathematics, a well-defined expression or unambiguous expression is an expression whose definition assigns it a unique interpretation or value. Otherwise, the expression is said to be not well defined, ill defined or ambiguous. [1]
The x-coordinates of the red circles are stationary points; the blue squares are inflection points. In mathematics, a critical point is the argument of a function where the function derivative is zero (or undefined, as specified below). The value of the function at a critical point is a critical value. [1]