# Definition:Free Variable/Predicate Logic

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## Definition

In predicate logic, a **free variable** is a variable which exists in a WFF only as free occurrences.

## 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

- 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.