Definition:Universal Quantifier

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

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

That is:


 * $$\forall x:$$ means: "For all objects $$x$$, it is true that ...".

Some authors use $$\left({x}\right)$$ to mean $$\forall x$$, but the bespoke symbol is usually preferred as there is then no room for ambiguity.

Also see

 * Universal statement.