reciproche

Reciproque (réciproque in French) is a term used across mathematics, logic, and linguistics to denote concepts of mutuality or inversion. It can refer to reciprocal numbers, inverse relations, or the converse of a conditional statement, depending on the context. The underlying idea is a two-way or reversing relationship between entities or operations.

In mathematics, the reciprocal of a nonzero number x is 1/x, since x·(1/x) = 1. The reciprocal concept also appears in inverses: the inverse of a function f is a function g such that g(f(x)) = x for all x in the domain, and the inverse relation R^{-1} of a relation R is defined by a R^{-1} b iff b R a. A function has an inverse only if it is bijective.

In logic, la réciproque of a conditional statement p → q is the statement q → p. The réciproque is not generally equivalent to the original implication and may have a different truth value.

In linguistics and semantics, réciproque can denote mutual relations or reciprocal actions between participants, such as reciprocal pronouns or verbs that encode mutuality. As an adjective, réciproque means mutual or two-way, as in reciprocal arrangements or reciprocal rights.

Etymology: from Latin reciprocus, from recipere “to take back,” via French réciproque.