improper

Improper is an adjective and, in some contexts, an adverb meaning not proper, inappropriate, or not in accordance with accepted standards or rules. It can describe behavior, dress, conduct, arguments, or procedures that are considered unsuitable in a given social, professional, or legal context. The term often carries a negative connotation, implying a violation of norms, etiquette, or formal requirements. In formal writing, phrases such as improper conduct or improper procedure flag deviations from established rules.

In mathematics, improper has several technical senses. The term is used most commonly for improper fractions, where the numerator is greater than or equal to the denominator, such as 7/3. These may be treated as improper fractions or rewritten as mixed numbers.

An improper integral is an integral in which either the interval is unbounded or the integrand has a nonremovable discontinuity within the interval. Such integrals are defined as limits of proper integrals, and they may converge to a finite value or diverge to infinity.

In statistics, an improper prior is a prior distribution that does not integrate to one. It can serve as a non-informative or objective prior in Bayesian analysis, often used to reflect lack of prior knowledge. When combined with data, the resulting posterior distribution is typically proper if the likelihood is informative enough.

See also: proper.