The inequality formula of absolute value can be decomposed into two parts. The inequality on the left |||| A |-| B|||≤| AB | describes the first characteristic of absolute inequality, that is, the difference between the absolute values of two numbers is not greater than the sum or difference of these two numbers. The inequality | a b | ≤| a |+b | on the right describes the second characteristic of absolute inequality, that is, the absolute value of the sum or difference of two numbers will not be greater than the sum or difference of the absolute values of these two numbers.
Absolute inequality formula can be used to describe the range of a variable. Specifically, if a variable x satisfies an absolute inequality, then the value range of this variable is between -a and a, where a is a positive real number.
Absolute inequality formula is also used to solve some complex mathematical problems, such as solving partial differential equations and solving linear programming. At the same time, in the engineering field, the absolute inequality formula is also widely used, for example, in machine learning, it can be used to describe the size of the model attenuation rate.
Application fields of absolute inequality formula;
1, number axis comparison: absolute inequality can be used to compare the size relationship between two numbers. If a and b are two real numbers, then when a >；; ; B | a | & gt； B, and vice versa, which allows us to prove the size relationship of some numbers with absolute inequality.
2. Distance problem: In geometry, absolute inequality can be used to solve some distance problems. For example, in two-dimensional or three-dimensional space, the distance between two points can be calculated by Euclidean distance formula, which involves absolute inequality.
3. Maximum problem: Absolute inequality can be used to find the maximum of some functions. For example, for real number X, the function f (x) = | x-1| x-2 |+| x-3 |+...+| x-n | is (n- 1)n/2, and this result can be proved by absolute inequality.
4. Probability statistics: In probability statistics, absolute inequality can be used to calculate the probability of some events, or to test whether some assumptions are true. For example, absolute inequality can be used to prove some theorems of large numbers, so as to calculate the probability of events.
5. Numerical calculation: In numerical calculation, absolute inequality can be used to estimate the error. For example, when we use a computer to calculate some mathematical problems, we may get some approximate results due to the accuracy limitation of the computer. Using absolute inequalities, we can estimate the errors of these approximate results.