Definition:Free Occurrence

Definition
Let $\mathcal L_1$ be the language of predicate logic.

Let $\mathbf A$ be a WFF of $\mathcal L_1$.

An occurrence of a variable $x$ in $\mathbf A$ is said to be a free occurrence it is not bound.

Also known as
Some authors gloss over the difference between:
 * a free variable: a variable which exists in a WFF only as free occurrences

and:
 * a free occurrence of a variable which may otherwise exist as a bound variable.

Also see

 * Definition:Occurrence (Formal Systems)
 * Definition:Bound Occurrence, the complementary notion
 * Definition:Alphabetic Substitution