Universal Quantifier

#Math

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

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