\begin{definition}[Definition:Existential Quantifier]
The symbol $\exists$ is called the '''existential quantifier'''.
It expresses the fact that, in a particular universe of discourse, there exists (at least one) object having a particular property.
That is:
:$\exists x:$
means:
:'''There exists at least one object $x$ such that ...'''
In the language of set theory, this can be formally defined:
:$\exists x \in S: \map P x := \set {x \in S: \map P x} \ne \O$
where $S$ is some set and $\map P x$ is a propositional function on $S$.
\end{definition}