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The graph of y = ln x. Any monotonically increasing function, by its definition, [9] may be applied to both sides of an inequality without breaking the inequality relation (provided that both expressions are in the domain of that function). However, applying a monotonically decreasing function to both sides of an inequality means the inequality ...
The expression on the right side of the "=" sign is the right side of the equation and the expression on the left of the "=" is the left side of the equation. For example, in + = + x + 5 is the left-hand side (LHS) and y + 8 is the right-hand side (RHS).
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.
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
A signed graph is the special kind of gain graph in which the gain group has order 2. The pair (G, B(Σ)) determined by a signed graph Σ is a special kind of biased graph. The sign group has the special property, not shared by larger gain groups, that the edge signs are determined up to switching by the set B(Σ) of balanced cycles. [19]
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.
Jensen's inequality generalizes the statement that a secant line of a convex function lies above its graph. Visualizing convexity and Jensen's inequality. In mathematics, Jensen's inequality, named after the Danish mathematician Johan Jensen, relates the value of a convex function of an integral to the integral of the convex function.
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