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Inequation
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In mathematics, an inequation is a statement that an inequality holds between two values. It is usually written in the form of a pair of expressions denoting the values in question, some examples of inequations are, a < b, x + y + z ≤1, n >1, x ≠0. Some authors apply the term only to inequations in which the inequality relation is, specifically, a shorthand notation is used for the conjunction of several inequations involving common expressions, by chaining them together. For example, the chain 0 ≤ a < b ≤1 is shorthand for 0 ≤ a a n d a < b a n d b ≤1. Similar to equation solving, inequation solving means finding what values 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, to be precise, what is sought are often not necessarily actual values, but, more in general, mathematical expressions. Often, an additional objective expression is given that is to be minimized by an optimal solution, see Linear programming#Example for a larger example. Computer support in solving inequations is described in constraint programming, in particular, the programming language Prolog III supports solving algorithms for particular classes of inequalities as a basic language feature, see constraint logic programming. F < g ⇔ { f ≥0 g >0 f <2 Equation Equals sign Inequality Relational operator