In mathematics, a uniqueness theorem, also called a unicity theorem, is a theorem asserting the uniqueness of an object satisfying certain conditions, or the equivalence of all objects satisfying the said conditions.[1] Examples of uniqueness theorems include:
Cauchy's rigidity theorem and Alexandrov's uniqueness theorem for three-dimensional polyhedra.
Black hole uniqueness theorem
Cauchy–Kowalevski theorem is the main local existence and uniqueness theorem for analytic partial differential equations associated with Cauchy initial value problems.
Cauchy–Kowalevski–Kashiwara theorem is a wide generalization of the Cauchy–Kowalevski theorem for systems of linear partial differential equations with analytic coefficients.
Division theorem, the uniqueness of quotient and remainder under Euclidean division.
Fundamental theorem of arithmetic, the uniqueness of prime factorization.
Holmgren's uniqueness theorem for linear partial differential equations with real analytic coefficients.
Picard–Lindelöf theorem, the uniqueness of solutions to first-order differential equations.
Thompson uniqueness theorem in finite group theory.
Uniqueness theorem for Poisson's equation.[2]
Electromagnetism uniqueness theorem for the solution of Maxwell's equation.
Uniqueness case in finite group theory.
The word unique is sometimes replaced by essentially unique, whenever one wants to stress that the uniqueness is only referred to the underlying structure, whereas the form may vary in all ways that do not affect the mathematical content.[1]
A uniqueness theorem (or its proof) is, at least within the mathematics of differential equations, often combined with an existence theorem (or its proof) to a combined existence and uniqueness theorem (e.g., existence and uniqueness of solution to first-order differential equations with boundary condition).[3]
^ abWeisstein, Eric W. "Uniqueness Theorem". mathworld.wolfram.com. Retrieved 2019-11-29.
Holmgren's uniquenesstheorem for linear partial differential equations with real analytic coefficients. Picard–Lindelöf theorem, the uniqueness of solutions...
mathematics, the fundamental theorem of arithmetic, also called the unique factorization theorem and prime factorization theorem, states that every integer...
The electromagnetism uniquenesstheorem states the uniqueness (but not necessarily the existence) of a solution to Maxwell's equations, if the boundary...
non-Lipschitz functions at their ending time, they are not included in the uniquenesstheorem of solutions of Lipschitz differential equations. As example, the...
named after Euclid, it seems that he did not know the existence and uniquenesstheorem, and that the only computation method that he knew was the division...
and uniquenesstheorems are usually important organizational principles. In many introductory textbooks, the role of existence and uniquenesstheorems for...
original uniquenesstheorem (Feit & Thompson 1963, theorems 24.5 and 25.2) states that in a minimal simple finite group of odd order there is a unique maximal...
two well-known uniquenesstheorems for Leavitt path algebras: the graded uniquenesstheorem and the Cuntz-Krieger uniquenesstheorem. These are analogous...
proof Constructivism (philosophy of mathematics) Uniquenesstheorem "Definition of existence theorem | Dictionary.com". www.dictionary.com. Retrieved...
region. Watson's theorem and Carleman's theorem show that Borel summation produces such a best possible sum of the series. Watson's theorem gives conditions...