Ungleich

Ungleich is a German term meaning not equal. As an adjective, it describes a lack of equality between two entities, quantities, or values. In everyday language it can refer to differences, while in mathematics it is used to express inequality.

In mathematical usage, Ungleich is part of phrases that state that two quantities are not the same. The corresponding noun is Ungleichheit, which denotes the concept of inequality. The standard mathematical notation for Ungleich is the not-equal symbol, ≠, and, in programming, often !=. For example, a ist ungleich b means a ≠ b.

Common examples include statements like 2 ist ungleich 3 (2 ≠ 3) or x ist ungleich 0 (x ≠ 0). Ungleich can apply to numbers, variables, expressions, or functions, and appears in the context of equations, inequalities, and logical relations. It is also used in discussions of bounds and comparisons, such as lineare Ungleichungen and verschiedene Ungleichheiten, where relationships are constrained by greater-than or less-than conditions.

Beyond pure mathematics, Ungleichheit has broader sociocultural usage. Ungleichheit (inequality) describes disparities in areas such as income, access to resources, and opportunities, often discussed in social sciences and public policy. The term contrasts with Gleichheit (equality), and together they frame many mathematical, logical, and societal discussions about similarity, difference, and fairness. See also Gleichheit, Ungleichung, and Ungleichheit in social contexts.