Uniqueness theorem

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In mathematics, a uniqueness theorem is a theorem proving that certain conditions determine a unique solution. Examples of uniqueness theorems include:

A theorem, also called a unicity theorem, stating the uniqueness of a mathematical object, which usually means that there is only one object fulfilling given properties, or that all objects of a given class are equivalent (i.e., they can be represented by the same model). This is often expressed by saying that the object is uniquely determined by a certain set of data. 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.

A uniqueness theorem / proof is, at least within mathematics of differential equations, often combined with an existence theorem / proof to a combined existence and uniqueness theorem.

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