# Definition:String

## Definition

Let $\AA$ be an alphabet of symbols.

A string (in $\AA$) is a sequence of symbols from $\AA$.

There is no limit to the number of times a particular symbol may appear in a given string.

### Finite String

A string $S$ in $\AA$ is a finite string if and only if the sequence of symbols of which it is composed is finite.

### Infinite String

A string $S$ in $\AA$ is an infinite string if and only if the sequence of symbols of which it is composed is infinite.

## Also defined as

Some sources use the word string to mean a finite string, that is, what is defined on $\mathsf{Pr} \infty \mathsf{fWiki}$ as a word.