## ::Uniqueness quantification

### ::concepts

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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

- <math>\exists! n \in \mathbb{N}\,(n - 2 = 4)</math>

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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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

- <math>\exists! n \in \mathbb{N}\,(n - 2 = 4)</math>

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

PREVIOUS: Intro | NEXT: Proving uniqueness |

<< | >> |