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In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. [ 1 ] It is used most often to compare two numbers on the number line by their size. The main types of inequality are less than and greater than.
Inequation. In mathematics, an inequation is a statement that an inequality holds between two values. [1][2] It is usually written in the form of a pair of expressions denoting the values in question, with a relational sign between them indicating the specific inequality relation. Some examples of inequations are:
Linear inequality. In mathematics a linear inequality is an inequality which involves a linear function. A linear inequality contains one of the symbols of inequality: [1] < less than. > greater than. ≤ less than or equal to. ≥ greater than or equal to. ≠ not equal to.
Cauchy–Schwarz inequality. The Cauchy–Schwarz inequality (also called Cauchy–Bunyakovsky–Schwarz inequality) [1][2][3][4] is an upper bound on the inner product between two vectors in an inner product space in terms of the product of the vector norms. It is considered one of the most important and widely used inequalities in mathematics.
Bhatia–Davis inequality, an upper bound on the variance of any bounded probability distribution. Bernstein inequalities (probability theory) Boole's inequality. Borell–TIS inequality. BRS-inequality. Burkholder's inequality. Burkholder–Davis–Gundy inequalities. Cantelli's inequality. Chebyshev's inequality.
In mathematics, a law is a formula that is always true within a given context. [1] Laws describe a relationship, between two or more terms or expressions (which may contain variables), usually using equality or inequality, [2] or between formulas themselves, for instance, in mathematical logic.
In mathematics, Young's inequality for products is a mathematical inequality about the product of two numbers. [1] The inequality is named after William Henry Young and should not be confused with Young's convolution inequality. Young's inequality for products can be used to prove Hölder's inequality. It is also widely used to estimate the ...
Visual proof that (x + y)2 ≥ 4xy. Taking square roots and dividing by two gives the AM–GM inequality. [1] In mathematics, the inequality of arithmetic and geometric means, or more briefly the AM–GM inequality, states that the arithmetic mean of a list of non-negative real numbers is greater than or equal to the geometric mean of the same ...