equivalent

Equivalent describes a relation of sameness in value, function, or meaning within a specified context. Two things are equivalent if one can substitute for the other without changing the outcome, given the rules of the framework in which they are used.

In mathematics, an equivalence relation is reflexive, symmetric, and transitive. If a ~ b and b ~ c, then a ~ c, partitioning a set into equivalence classes. Common examples include congruence modulo n (a ≡ b mod n) and equality under an isomorphism, where objects are considered the same in structure even if they are not identical.

In logic, two statements are logically equivalent if they have the same truth value in all situations; written p ↔ q and read as "p if and only if q." Equivalence in mathematics often means the two objects are interchangeable under a mapping, not necessarily identical.

In science and everyday language, equivalent appears in chemistry as equivalent weight, a measure used in balancing reactions, and in pharmacology as bioequivalence, indicating similar biological effects under defined conditions. The term also appears in physics in concepts such as the equivalence principle, which relates gravitational and inertial phenomena.

Etymology traces to Latin aequivalens, meaning "of equal value," highlighting substitutability within a framework rather than universal sameness.