Uligheden

Uligheden is a Danish term meaning "the inequality" and is used to refer to statements about relative size or order of quantities. In mathematics it denotes a relation in which one quantity is not equal to another, usually indicating that one side is larger or smaller than the other. In social sciences, it describes disparities in distributions such as income, wealth, or opportunities.

In mathematics, inequalities are foundational tools that provide bounds and estimates. They appear in analysis, geometry, algebra, and probability. Classic examples include the triangle inequality, which states that the absolute value of a sum is not greater than the sum of the absolute values; the AM-GM inequality, which relates the arithmetic and geometric means for nonnegative numbers; and the Cauchy–Schwarz inequality, which bounds the inner product of vectors. Inequalities help prove convergence, stability, and optimality across many areas of math.

In economics and related fields, the study of inequality focuses on how resources and outcomes are distributed within a society. Common measures include the Gini coefficient, the Theil index, and the Palma ratio. Researchers analyze the drivers of disparities—such as differences in skills, capital ownership, institutions, or access to education and health—and assess policy options like taxation, transfers, education, and social protection to influence distributions.

Uligheden thus covers a broad concept, linking precise mathematical relations with empirical questions about fairness and distribution in society. See also inequality (mathematics), economic inequality, and related measures of distribution.