# Definition:Word (Formal Systems)

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*This page is about a finite string of symbols from a given alphabet. For other uses, see Definition:Word.*

## Contents

## Definition

Let $\mathcal A$ be an alphabet.

Then a **word in $\mathcal A$** is a juxtaposition of finitely many (primitive) symbols of $\mathcal A$.

**Words** are the most ubiquitous of collations used for formal languages.

## Also known as

Different treatments of formal languages use different terms for **word**.

Examples include **formula**, **sentence** and **string**.

However, these alternatives conflict with the concepts logical formula, sentence and string, respectively, in the scope of this site; therefore, their use is discouraged.

It is useful to note that in this context **word** is a synonym for finite string.

## Also see

- Definition:Well-Formed Word: a
**word**in $\mathcal A$ admitted by the formal grammar of some formal language - Definition:Collation: a generalization of a
**word**as a means to present information in a structured manner

## Sources

- 1965: E.J. Lemmon:
*Beginning Logic*... (previous) ... (next): $\S 2.1$: Formation Rules (in the context of the language of propositional logic) - 1996: H. Jerome Keisler and Joel Robbin:
*Mathematical Logic and Computability*... (previous) ... (next): $\S 1.2$: Syntax of Propositional Logic