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The absolute difference of two real numbers and is given by | |, the absolute value of their difference. It describes the distance on the real line between the points corresponding to x {\displaystyle x} and y {\displaystyle y} .
The actual difference is not usually a good way to compare the numbers, in particular because it depends on the unit of measurement. For instance, 1 m is the same as 100 cm, but the absolute difference between 2 and 1 m is 1 while the absolute difference between 200 and 100 cm is 100, giving the impression of a larger difference. [4]
The difference of two squares is used to find the linear factors of the sum of two squares, using complex number coefficients. For example, the complex roots of z 2 + 4 {\displaystyle z^{2}+4} can be found using difference of two squares:
Numbers p and q like this can be computed with the extended Euclidean algorithm. gcd(a, 0) = | a |, for a ≠ 0, since any number is a divisor of 0, and the greatest divisor of a is | a |. [2] [5] This is usually used as the base case in the Euclidean algorithm. If a divides the product b⋅c, and gcd(a, b) = d, then a/d divides c.
The simplest method is to use finite difference approximations. A simple two-point estimation is to compute the slope of a nearby secant line through the points (x, f(x)) and (x + h, f(x + h)). [1] Choosing a small number h, h represents a small change in x, and it can be either positive or negative.
Every other triangular number is a hexagonal number. Knowing the triangular numbers, one can reckon any centered polygonal number; the n th centered k-gonal number is obtained by the formula = + where T is a triangular number. The positive difference of two triangular numbers is a trapezoidal number.
where is the number of terms in the progression and is the common difference between terms. The formula is essentially the same as the formula for the standard deviation of a discrete uniform distribution, interpreting the arithmetic progression as a set of equally probable outcomes.
Catastrophic cancellation occurs when two numbers which are approximately equal are subtracted. While each of the numbers may independently be representable to a certain number of digits of precision, the identical leading digits of each number cancel, resulting in a difference of lower relative precision.