Uniqueness quantification

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In mathematics and logic, the term "uniqueness" refers to the property of being the one and only object satisfying a certain condition.^[1] This sort of quantification is known as uniqueness quantification or unique existential quantification, and is often denoted with the symbols "∃!"^[2] or "∃₌₁". It is defined to mean there exists an object with the given property, and all objects with this property are equal.

For example, the formal statement

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

may be read as "there is exactly one natural number ${\displaystyle n}$ such that ${\displaystyle n-2=4}$".