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Two-dimensional linear inequalities are expressions in two variables of the form: + < +, where the inequalities may either be strict or not. The solution set of such an inequality can be graphically represented by a half-plane (all the points on one "side" of a fixed line) in the Euclidean plane. [2]
Unequal educational outcomes are attributed to several variables, including family of origin, gender, and social class. Achievement, earnings, health status, and political participation also contribute to educational inequality within the United States and other countries. [10]
Later researchers built on Bell's work by proposing new inequalities that serve the same purpose and refine the basic idea in one way or another. [ 5 ] [ 6 ] Consequently, the term "Bell inequality" can mean any one of a number of inequalities satisfied by local hidden-variables theories; in practice, many present-day experiments employ the ...
Bennett's inequality, an upper bound on the probability that the sum of independent random variables deviates from its expected value by more than any specified amount; Bhatia–Davis inequality, an upper bound on the variance of any bounded probability distribution; Bernstein inequalities (probability theory) Boole's inequality; Borell–TIS ...
It is considered one of the most important and widely used inequalities in mathematics. [5] Inner products of vectors can describe finite sums (via finite-dimensional vector spaces), infinite series (via vectors in sequence spaces), and integrals (via vectors in Hilbert spaces). The inequality for sums was published by Augustin-Louis Cauchy .
When researchers use quantitative variables such as income or wealth to measure inequality, on an examination of the data, patterns are found that indicate these other social variables contribute to income or wealth as intervening variables. Significant inequalities in income and wealth are found when specific socially defined categories of ...
Instead, the inequalities must be solved independently, yielding x < 1 / 2 and x ≥ −1 respectively, which can be combined into the final solution −1 ≤ x < 1 / 2 . Occasionally, chained notation is used with inequalities in different directions, in which case the meaning is the logical conjunction of the inequalities ...
Following Antman (1983, p. 283), the definition of a variational inequality is the following one.. Given a Banach space, a subset of , and a functional : from to the dual space of the space , the variational inequality problem is the problem of solving for the variable belonging to the following inequality: