Uniqueness theorem

From Wikipedia, the free encyclopedia

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:

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]

See also[edit]


  1. ^ a b Weisstein, Eric W. "Uniqueness Theorem". mathworld.wolfram.com. Retrieved 2019-11-29.
  2. ^ "The uniqueness theorem". farside.ph.utexas.edu. Retrieved 2019-11-29.
  3. ^ "Existence and Uniqueness". www.sosmath.com. Retrieved 2019-11-29.