Existential Quantification

A logical quantifier expressed as: $\exists x\in X,P(x)$ Meaning “there exists an $x$ in $X$ such that $P(x)$ is true.” Analogous to a logical disjunction ($\bigvee$) over all elements.

Context

Existential quantification is one of two fundamental quantifiers in predicate logic (the other being universal quantification). For example, $\exists x\in \mathbb{Z},x^2=4$ is true because $x=2$ satisfies it.

See Also

• universal quantification
• there exists
• for all
• existence statements
• existence theorems