Inequality

An inequality is a mathematical statement that compares quantities using relations such as less than, greater than, or not equal to. It can describe a range of values that satisfy a condition.

Order relation: A relation that arranges elements according to a notion of precedence or magnitude. Inequality symbols express order relations between quantities.
Inequality sign reversal: The reversal of an inequality's direction when both sides are multiplied or divided by a negative number. This rule is the key exception to ordinary equation-solving transformations.
Linear programming: An optimization method that maximizes or minimizes a linear objective subject to linear constraints. Its feasible region is defined by simultaneous inequalities.
Equation: A mathematical statement asserting that two expressions have equal values. Unlike an equation, an inequality generally describes an ordered range of values.
Real number: A number on the continuous number line, including rational and irrational numbers. Most elementary inequalities compare real numbers or expressions taking real values.
Linear inequality: An inequality whose expressions are linear in their variables. Its solution follows from isolating variables while preserving comparison direction.
Optimization: The mathematical study of choosing the best feasible value of an objective. Inequalities specify feasible choices and bounds on optimal values.
Not equal: A comparison asserting that two quantities have different values, without specifying which is larger. It excludes equality but does not establish an order between the quantities.
Variable: A symbol that represents a quantity whose value may be unknown or change. Variables let an inequality state which values satisfy a comparison.
Compound inequality: A statement combining two or more inequalities with logical connectors such as and or or. It combines bounds to describe intervals or unions of intervals.

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