Set of Finite Strings/Examples

Examples of Sets of Finite Strings

Over One Element

Let $\Sigma$ be the alphabet defined as:

$\Sigma = \set a$

Then the set of finite strings $\Sigma^*$ over $\Sigma$ is:

$\Sigma^* = \set {\epsilon, a, aa, aaa, aaaa, \ldots}$

where $\epsilon$ denotes the null string.

Over Two Elements

Let $\Sigma$ be the alphabet defined as:

$\Sigma = \set {0, 1}$

Then the set of finite strings $\Sigma^*$ over $\Sigma$ is:

$\Sigma^* = \set {\epsilon, 0, 1, 00, 01, 10, 11, 000, 001, \ldots}$

where $\epsilon$ denotes the null string.