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Kunita–Watanabe inequality; Le Cam's theorem; Lenglart's inequality; Marcinkiewicz–Zygmund inequality; Markov's inequality; McDiarmid's inequality; Paley–Zygmund inequality; Pinsker's inequality; Popoviciu's inequality on variances; Prophet inequality; Rao–Blackwell theorem; Ross's conjecture, a lower bound on the average waiting time ...
The feasible regions of linear programming are defined by a set of inequalities. 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.
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: <
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; A linear inequality looks exactly like a linear equation, with the inequality sign replacing the equality sign.
In mathematics, the QM-AM-GM-HM inequalities, also known as the mean inequality chain, state the relationship between the harmonic mean, geometric mean, arithmetic mean, and quadratic mean (also known as root mean square). Suppose that ,, …, are positive real numbers. Then
Many important inequalities can be proved by the rearrangement inequality, such as the arithmetic mean – geometric mean inequality, the Cauchy–Schwarz inequality, and Chebyshev's sum inequality. As a simple example, consider real numbers : By applying with := for all =, …,, it follows that + + + + + + for every permutation of , …,.
Carleman's inequality; Cauchy–Schwarz inequality; Chebyshev–Markov–Stieltjes inequalities; Chebyshev's sum inequality; Christ–Kiselev maximal inequality; CHSH inequality; Clarkson's inequalities; Cohn-Vossen's inequality; Correlation inequality; Cotlar–Stein lemma; Crossing number inequality
An illustration of Bernoulli's inequality, with the graphs of = (+) and = + shown in red and blue respectively. Here, r = 3. {\displaystyle r=3.} In mathematics , Bernoulli's inequality (named after Jacob Bernoulli ) is an inequality that approximates exponentiations of 1 + x {\displaystyle 1+x} .