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Existential quantifier

An existential quantifier is the symbol ∃ in predicate calculus. It roughly represents the phrase "for some" or "there exists". For example

∃ x (x2=25)
means "there exists an x such that x2=25".

The unique existential quantifer is the symbol ∃!. For example,

∃! x (x-2) = 4

means "there exists an unique x such that x-2 = 4".

     History of the Quantifer  

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See Existential quantification for details.