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 denoted with the symbol "?!". For example, the formal statement exists! n in mathbb,(n - 2 = 4) may be read aloud as "there is exactly one natural number n such that n - 2 = 4". Reduction to ordinary existential and universal quantification Generalizations One generalization of uniqueness quantification is counting quantification. This includes both quantification of the form "exactly k objects exist such that ..." as well as "infinitely many objects exist such that ..." and "only finitely many object exist such that...".

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