Impróprios

Impróprios is the plural form of impróprio, an adjective in Portuguese that denotes something that is not appropriate, suitable, or belonging to the usual category. The term is used across different domains to indicate a lack of fit or propriety in a given context, and can refer to mathematical concepts as well as everyday language.

In mathematics, the expression frações impróprias (improper fractions) describes fractions whose numerator is greater than or equal to the denominator. For example, 7/4 and 9/9 are impróprias. Such fractions can be converted to mixed numbers (7/4 = 1 e 3/4), and they contrast with frações próprias, where the numerator is smaller than the denominator. The concept is common in elementary arithmetic and pre-algebra.

In statistics and probability, the term priors impróprios (improper priors) refers to prior distributions that do not integrate to 1 over their domain. They are often used to express non-informative or vague prior information, particularly when there is limited prior knowledge. However, improper priors can lead to problematic or undefined posteriors if the likelihood is not sufficiently informative, requiring careful theoretical handling.

In everyday language, impróprios describes actions, remarks, or behaviors that are not appropriate for a given situation. Phrases like comportamento impróprio or comentário impróprio are used to signal a breach of social norms or professional standards. Overall, the term signals a mismatch between what is expected and what is observed.