Inequality is a mathematical term, which refers to the inequality represented by inequality symbols. Inequalities can be divided into strict inequalities and non-strict inequalities. Strict inequality is defined by >: and; 1 and 3
Non-strict inequality is the expression of inequality ≥ and ≤, such as 2≥ 1, 3≤4. In non-strict inequalities, the values on both sides of the inequality sign can be equal. In addition to the above two inequalities, there is a special inequality, namely ≦, which means that two values are not equal, for example, 2≠3.
Inequalities are widely used in mathematics, such as solving equations, finding the range of functions and judging the monotonicity of functions. In addition, in real life, inequalities are also widely used, such as investment, production, consumption and so on.
When solving inequality problems, we usually use some basic properties and methods, such as transitivity, addition, multiplication, addition of the same inequality, multiplication of the same inequality and so on. These properties and methods can help us solve inequality problems more simply and accurately.
Other applications of inequality in mathematics;
1. linear programming: linear programming is a mathematical method used to find the maximum or minimum value of an objective function under a set of linear inequalities. Linear programming is widely used in economy, management, engineering and other fields, such as production planning, resource allocation, transportation and so on.
2. Probability theory and mathematical statistics: In probability theory and mathematical statistics, inequalities are widely used in the comparison of random variables, the law of large numbers, the central limit theorem and so on. For example, Chebyshev inequality can be used to estimate the range of random variables, and Markov inequality can be used to estimate the mathematical expectation of random variables.
3. Calculus: In calculus, inequalities are widely used in the study of monotonicity, convexity and extremum of functions. For example, the mean value theorem can be used to prove some inequalities, the Lobida rule can be used to find some limits, and the Taylor formula can be used to estimate some errors.