Existential Quantifier

#Math

$\displaystyle ~\exists~x:P(x)\equiv P(x_{1})\lor P(x_{2})\lor\ldots P(x_{n})\lor\dots$

• $\displaystyle P(x)$ is a predicate
• The truth value of the statement "there exists x such that $\displaystyle P(x)$ is true" is the same as $\displaystyle P(x_{1})$ is true or $\displaystyle P(x_{n})$ for all other $\displaystyle n$ is true