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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:
The feasible regions of linear programming are defined by a set of inequalities. In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. [1] It is used most often to compare two numbers on the number line by their size.
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
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.
Another type of equation is inequality. Inequalities are used to show that one side of the equation is greater, or less, than the other. The symbols used for this are: > where > represents 'greater than', and < where < represents 'less than'. Just like standard equality equations, numbers can be added, subtracted, multiplied or divided.
Reducing and re-arranging the coefficients by adding multiples of as necessary, we can assume < (in fact, this is the unique such satisfying the equation and inequalities). Similarly we take u , v {\displaystyle u,v} satisfying N − k = u a + v b {\displaystyle N-k=ua+vb} and 0 ≤ u < b {\displaystyle 0\leq u<b} .