Category:Definitions/Universal Quantifier

This category contains definitions related to the universal quantifier.
Related results can be found in Category:Universal Quantifier.

The symbol $\forall$ is called the universal quantifier.

It expresses the fact that, in a particular universe of discourse, all objects have a particular property.

That is:

$\forall x:$

means:

For all objects $x$, it is true that ...

In the language of set theory, this can be formally defined:

$\forall x \in S: \map P x := \set {x \in S: \map P x} = S$

where $S$ is some set and $\map P x$ is a propositional function on $S$.