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If a relation is transitive then its transitive extension is itself, that is, if R is a transitive relation then R 1 = R. The transitive extension of R 1 would be denoted by R 2, and continuing in this way, in general, the transitive extension of R i would be R i + 1. The transitive closure of R, denoted by R* or R ∞ is the set union of R, R ...
Similar to equation solving, inequation solving means finding what values (numbers, functions, sets, etc.) fulfill a condition stated in the form of an inequation or a conjunction of several inequations. These expressions contain one or more unknowns, which are free variables for which values are sought that cause the condition to be fulfilled ...
Symbolab is an answer engine [1] that provides step-by-step solutions to mathematical problems in a range of subjects. [2] It was originally developed by Israeli start-up company EqsQuest Ltd., under whom it was released for public use in 2011.
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
When Ω is a ball, the above inequality is called a (p,p)-Poincaré inequality; for more general domains Ω, the above is more familiarly known as a Sobolev inequality. The necessity to subtract the average value can be seen by considering constant functions for which the derivative is zero while, without subtracting the average, we can have ...
Equation number: 2: The number of the equation, also used to generate the anchor. String: suggested: Anchor id: id: The anchor id. If you set this to "my-eqn" (no quotes), the link [[#my-eqn|see my equation]] will take you to the equation. Default Defaults to "equation-" + the equation number, if that is specified. String: optional
The Foster–Greer–Thorbecke indices are a family of poverty metrics.The most commonly used index from the family, FGT 2, puts higher weight on the poverty of the poorest individuals, making it a combined measure of poverty and income inequality and a popular choice within development economics.