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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
An inequality is said to be sharp if it cannot be relaxed and still be valid in general. Formally, a universally quantified inequality φ is called sharp if, for every valid universally quantified inequality ψ, if ψ ⇒ φ holds, then ψ ⇔ φ also holds. For instance, the inequality ∀a ∈ R. a 2 ≥ 0 is sharp, whereas the inequality ∀ ...
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]
Ladyzhenskaya's inequality; Landau–Kolmogorov inequality; Landau-Mignotte bound; Lebedev–Milin inequality; Leggett inequality; Leggett–Garg inequality; Less-than sign; Levinson's inequality; Lieb–Oxford inequality; Lieb–Thirring inequality; Littlewood's 4/3 inequality; Log sum inequality; Łojasiewicz inequality; Lubell–Yamamoto ...
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:
There are three inequalities between means to prove. There are various methods to prove the inequalities, including mathematical induction, the Cauchy–Schwarz inequality, Lagrange multipliers, and Jensen's inequality. For several proofs that GM ≤ AM, see Inequality of arithmetic and geometric means.
When we recently wrote about the toughest math problems that have been solved, we mentioned one of the greatest achievements in 20th-century math: the solution to Fermat’s Last Theorem. Sir ...
In mathematics, the Newton inequalities are named after Isaac Newton. Suppose a 1, a 2, ..., a n are non-negative real numbers and let denote the kth elementary symmetric polynomial in a 1, a 2, ..., a n. Then the elementary symmetric means, given by = (),