Impróprias

Impróprias is the feminine plural form of imprópria, an adjective in Portuguese meaning not proper, improper, or inappropriate. It is used to describe feminine nouns and is part of a system of gender and number agreement. The masculine singular form is impróprio, the feminine singular imprópria, the masculine plural impróprios, and the feminine plural impróprias.

In ordinary language, impróprias describes things considered unsuitable or inappropriate. Examples include informações impróprias (inappropriate information) or regras impróprias (improper rules). The term carries a normative sense, indicating that something does not meet expected or acceptable standards in a given context.

In mathematics, impróprias appears in several standard phrases. Frações impróprias are fractions where the numerator is greater than or equal to the denominator; they contrast with frações próprias, where the numerator is smaller. Frações impróprias can be converted to mixed numbers. Another common usage is integral imprópria (improper integral), referring to integrals with infinite limits or with integrands that have singularities within the interval of integration; these integrals are defined via limit processes to determine convergence or divergence.

Other specialized uses exist in fields that borrow the term from the broad sense of “not proper.” However, impróprias mainly appears in general language and in mathematical terminology as described above.

See also: impropriedade, impróprio, frações próprias, integrais impróprias.