# Definition:Bound Occurrence

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## Contents

## Definition

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

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

Let $Q x$ be an occurrence of a quantifier in $\mathbf A$.

Any occurrence of the variable $x$ in the scope of $Q$ is called a **bound occurrence**.

## Also known as

Some authors gloss over the difference between:

- a
**bound variable**: a variable which exists in a WFF only as**bound occurrences**

and:

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

## Also see

- Definition:Occurrence (Formal Systems)
- Definition:Free Occurrence, the complementary notion
- Definition:Alphabetic Substitution

- Definition:Bound Variable: a variable which occurs as a
**bound occurrence**

## Sources

- 1972: A.G. Howson:
*A Handbook of Terms used in Algebra and Analysis*... (previous) ... (next): $\S 1$: Some mathematical language: Variables and quantifiers - 1996: H. Jerome Keisler and Joel Robbin:
*Mathematical Logic and Computability*: $\S 2.3$ - 2009: Kenneth Kunen:
*The Foundations of Mathematics*... (previous) ... (next): $\mathrm{II}.5$ First-Order Logic Syntax: Definition $\mathrm{II}.5.5$