Quantifiers

Quantifiers are words, expressions, or phrases that indicate the number of elements that a statement pertains to. In mathematical logic, there are two quantifiers: the universal quantifier ("for all") and the existential quantifier ("there exists").

Universal quantifier: This quantifier is used to state a proposition that is true for all variables x of a given set. For example, the proposition "x^2 is a nonnegative number" is true for all real numbers, so we state "for all $x\in \mathbb {R}$, $x^{2}$ is nonnegative". Symbolically, we write the universal quantifier as $\forall$ (ex. $\forall x\in \mathbb {R} ,x^{2}\geq 0$).

Resources

• Quantifiers, Mathematics LibreTexts