Category:Definitions/Existential Quantifier

This category contains definitions related to Existential Quantifier.
Related results can be found in Category: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 $S$.