Editing Uniqueness quantification (section)

{{Short description|Logical quantifier}}
{{redirect|Unique (mathematics)|other uses|Unique (disambiguation)}}
{{More sources|date=November 2024}}
In [[mathematics]] and [[logic]], the term "uniqueness" refers to the property of being the one and only object satisfying a certain condition.<ref>{{Cite web|url=http://mathworld.wolfram.com/UniquenessTheorem.html|title=Uniqueness Theorem|last=Weisstein|first=Eric W.|website=mathworld.wolfram.com|language=en|access-date=2019-12-15}}</ref> This sort of [[Quantifier (logic)|quantification]] is known as '''uniqueness quantification''' or '''unique existential quantification''', and is often denoted with the symbols "[[Existential quantification|∃]]!"<ref>{{Cite web|url=https://www.whitman.edu/mathematics/higher_math_online/section02.05.html|title=2.5 Uniqueness Arguments|website=www.whitman.edu|access-date=2019-12-15}}</ref> or "∃<sub>=1</sub>". It is defined to mean [[there exists]] an object with the given property, and [[Universal quantification|all objects]] with this property are [[Equality (mathematics)|equal]].

For example, the formal statement

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

may be read as "there is exactly one natural number <math>n</math> such that <math>n - 2 =4</math>".