Universal and Existential Quantifiers.
The existential quantifier is \(\exists\) and is read “there exists” or “there is.” For example,
\begin{equation*}
\exists x (x \lt 0)
\end{equation*}
asserts that there is a number less than 0.
The universal quantifier is \(\forall\) and is read “for all” or “every.” For example,
\begin{equation*}
\forall x (x \ge 0)
\end{equation*}
asserts that every number is greater than or equal to 0.