Definition:Word (Formal Systems)

Definition
Let $\mathcal F$ be a formal language.

Let $\mathcal A$ be the alphabet of $\mathcal F$.

Then a word in $\mathcal A$ is defined as a finite string of symbols of $\mathcal A$.

Other Terms for the Same Concept
Different treatments of formal languages use different terms for this concept, for example:


 * Formula;
 * Sentence.

Some sources use the term string in this limited context.

Note
Not all words formed of symbols of $\mathcal A$ necessarily belong to $\mathcal F$.

Whether it does or not depends on the grammar of $\mathcal F$.

A word which does belong to $\mathcal F$ is sometimes called a well-formed word.