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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
For instance, to solve the inequality 4x < 2x + 1 ≤ 3x + 2, it is not possible to isolate x in any one part of the inequality through addition or subtraction. 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 .
The parameters most commonly appearing in triangle inequalities are: the side lengths a, b, and c;; the semiperimeter s = (a + b + c) / 2 (half the perimeter p);; the angle measures A, B, and C of the angles of the vertices opposite the respective sides a, b, and c (with the vertices denoted with the same symbols as their angle measures);
A simple procedure to determine which half-plane is in the solution set is to calculate the value of ax + by at a point (x 0, y 0) which is not on the line and observe whether or not the inequality is satisfied. For example, [3] to draw the solution set of x + 3y < 9, one first draws the line with equation x + 3y = 9 as a dotted line, to ...
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:
Boise's highest earners make at least 3.93 times that of the lowest earners. ... Aurora has an income inequality of 3.97. Those at the 80th percentile make $160,693, while those in the 20th ...
where , is the inner product.Examples of inner products include the real and complex dot product; see the examples in inner product.Every inner product gives rise to a Euclidean norm, called the canonical or induced norm, where the norm of a vector is denoted and defined by ‖ ‖:= , , where , is always a non-negative real number (even if the inner product is complex-valued).