Inequation

[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.

[2] A shorthand notation is used for the conjunction of several inequations involving common expressions, by chaining them together.

In rare cases, chains without such implications about distant terms are used.

[4] Similar to equation solving, inequation solving means finding what values (numbers, functions, sets, etc.)

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, expressions.

[5] For example, is a conjunction of inequations, partly written as chains (where

can be read as "and"); the set of its solutions is shown in blue in the picture (the red, green, and orange line corresponding to the 1st, 2nd, and 3rd conjunct, respectively).

Computer support in solving inequations is described in constraint programming; in particular, the simplex algorithm finds optimal solutions of linear inequations.

[6] The programming language Prolog III also supports solving algorithms for particular classes of inequalities (and other relations) as a basic language feature.

Usually because of the properties of certain functions (like square roots), some inequations are equivalent to a combination of multiple others.