Definition:Free Variable

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

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

In the context of predicate logic, $x$ is a free variable in $E$ if and only if it has not been introduced by a quantifier, either:

the universal quantifier $\forall$


the existential quantifier $\exists$.

Also known as

A free variable is often referred to as an unknown, particularly in mathematical contexts.

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 $\mathsf{Pr} \infty \mathsf{fWiki}$ is discouraged.

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

Also see