Uniqueness theorem

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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

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References

  1. 1 2 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.