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.