## ::Uniqueness quantification

### ::concepts

Exists::logic    Equality::first    Wedge::forall    There::exist    Assume::ordinary    Objects::''x''

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In mathematics and logic, the phrase "there is one and only one" is used to indicate that exactly one object with a certain property exists. In mathematical logic, this sort of quantification is known as uniqueness quantification or unique existential quantification.

Uniqueness quantification is often denoted with the symbols "∃!" or ∃=1". For example, the formal statement

$\exists! n \in \mathbb{N}\,(n - 2 = 4)$

may be read aloud as "there is exactly one natural number n such that n - 2 = 4".

Uniqueness quantification sections
Intro   Proving uniqueness    Reduction to ordinary existential and universal quantification    Generalizations    See also    References

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