nonunique

Nonunique is an adjective meaning not unique; it describes a result, solution, representation, or outcome that is not the only one of its kind. The term is used across disciplines to indicate a lack of a single, uniquely determined answer under given conditions.

In mathematics and related fields, nonuniqueness arises when a problem yields more than one distinct solution or representation. This is different from nonexistence (no solution) and from a unique solution (exactly one). Conditions that can cause nonuniqueness include underdetermined systems, symmetries in the problem, degeneracy, or insufficient constraints to pin down a single outcome.

Examples include linear systems with infinitely many solutions, where the solution set forms a subspace parameterized by free variables; equations with multiple roots, where several values satisfy the equation; and optimization problems where more than one point attains the same optimal value, leading to nonunique minimizers or maximizers.

In algebra, nonuniqueness often appears as nonunique factorization, where an element can be factored into irreducibles in more than one essentially different way. This concept underpins the study of factorization domains, class groups, and the ways in which arithmetic structure can vary between mathematical settings.

Nonuniqueness also arises in applied contexts due to model identifiability issues, measurement or modeling symmetry, or incomplete data. Recognizing nonuniqueness helps clarify what information is necessary to obtain a single conclusion and guides the interpretation of multiple valid outcomes.

See also: uniqueness, identifiability, well-posed problems.