# 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 if and only if 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.