Existential quantifier

A logical operation used in forming statements with the expression "for a certain x" ( "an x exists for which", "there exists an x such that" ). In formalized languages, existential quantifiers are denoted by $\exists x$, $(\exists x)$, $\cup_x$, $\vee_x$, $\Sigma_x$.

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The unique existential quantifier forms the assertion that "there exists exactly one x such that" and is denoted $\exists!x$.

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