NormE

Norme is a term used in several languages to denote a standard, rule, or measure. Its precise meaning varies by field, but it generally conveys notions of conformity, benchmarks, or prescribed norms. In French, norme often means a standard or guideline, and in mathematical writing the concept is typically called a norm (norme in French) when translated.

In mathematics, a norm is a function that assigns to each element of a vector space a non-negative length or size. A norm must satisfy positivity, homogeneity (scaling), and the triangle inequality. Common examples include the Euclidean norm, the Manhattan (L1) norm, and the maximum (L∞) norm. Norms induce metrics and underpin convergence, stability, and geometric structure in analysis and geometry.

In the social sciences, a social norm refers to an unwritten rule about expected behavior within a group or society. Norms guide actions, regulate conduct, and are reinforced through social approval or sanctions. They can vary across cultures and overtime, influencing everything from everyday etiquette to institutional practices.

In standardization and engineering, a norm or standard specifies requirements for products, services, or processes. Norms are produced by organizations such as ISO, IEC, and ASTM and can be normative (mandatory) or informative (descriptive). Compliance with norms promotes interoperability, safety, and quality across industries.

In language and philosophy, normative use describes prescriptions about correct language or conduct, distinguishing from descriptive accounts. The term is also used in ethics to denote principles about how people ought to act.