Definition:Free Variable

Definition
Let $x$ be a variable in an expression $E$.

$x$ is a free variable in $E$ it is not a bound variable.

In the context of predicate logic, $x$ is a free variable in $E$ it has not been introduced by a quantifier, either:
 * the universal quantifier $\forall$

or
 * the existential quantifier $\exists$.

Also known as
In the field of logic, a free variable can also be referred to as a real variable.

However, this can be confused with a variable whose domain is the set of real numbers, so its use on is discouraged.

The name arises in apposition to the name apparent variable, which is another name for bound variable.

Also see

 * Definition:Free Occurrence: a somewhat more precise concept, recognising the fact that a variable may appear multiple times in an expression, and not necessarily always of the same category.