Analytic number theory often operates with inequalities.

As in the case of equations, inequalities can be transformed in various ways. Astronomy a departure from uniform orbital motion Want to thank TFD for its existence?

The numbers a1, a2.

Diophantine approximations, an entire branch of number theory, are completely based on inequalities. Linear inequalities play a large role in the theory of linear programming.

The axiomatic development of inequalities is given in algebra. Click the link for more information. In geometry, inequalities are constantly encountered in the theory of convex bodies and in isoperimetric problems.

Multiplication or division by a negative number reverses the sign of the inequality; e. To solve such inequalities is to determine the limits within which the quantities entering into the inequalities must be taken in order for the inequalities to hold.

Differential inequalities are used in the theory of differential equations the Chaplygin method. Thus, an inequality remains valid if the same number is added to or subtracted from both sides.

The most famous inequality relates the harmonic mean, the geometric mean, the arithmetic mean, and the root-mean-square: We now give a few examples of important inequalities. The task of the theory of linear inequalities consists of studying the properties of this polyhedron.

In the theory of functions, various inequalities are constantly used for derivatives of polynomials and trigonometric polynomials. If the numbers A, B.

Certain problems in the theory of linear inequalities are closely related to the theory of best approximations, which was created by P.

The direction of the inequality remains unchanged if some number is added to both sides or subtracted from both sides or if both sides are multiplied or divided by some positive number; e.

Inequalities containing quantities that can assume different numerical values may be true for some values of these quantities and false for others. DictionaryThesaurusLegal. We can similarly multiply both sides of an inequality by a positive number. Inequalities have many properties in common with equalities.

Inequalities are very important in many branches of mathematics. In probability theory, many laws are formulated in terms of inequalities for example, the Chebyshev inequality. Link to this page: All these relations are termed inequalities.

For any real or complex numbers a1, a2.You can put this solution on YOUR website!-2>x Write a second inequality with the same meaningx> 2 or x+2 0 cheers, Stan H.

It contains the symbols, ≤, or ≥. To write an inequality, look for the following phrases to determine where to place the inequality symbol. Key Vocabulary inequality, p. solution of an inequality, p. solution set, p. graph of an inequality, p. EXAMPLE 1 Writing Inequalities Write the word sentence as an inequality.

a. Compound Inequalities A compound inequality is a sentence with two inequality statements joined either by the word “or” or by the word “and.” “And” indicates that both statements of the compound sentence are true at the same time.

The nicest way to write the solutions to the inequality is to write x > 3 again, but this time think of x > 3 as meaning "the set of all real numbers greater than 3." That's a fairly big set.

That's a fairly big set. Inequality definition is - the quality of being unequal or uneven: such as. How to use inequality in a sentence. See more words from the same century. Keep scrolling for more. More Definitions for inequality.

inequality. noun. English Language Learners Definition of inequality. In mathematics, an inequality is a relation that holds between two values when they are different (see also: equality). By the above laws, one can add or subtract the same number to all three terms, or multiply or divide all three terms by same nonzero number and reverse all inequalities if that number is negative.

DownloadWrite an inequality with the same meaning dictionary

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