Strings words over an Alphabet

Definition: Strings (words) over an Alphabet

From a formal point of view, an alphabet is a non-empty set, denoted by the Latin capital letter $\Sigma $ (“sigma”), whose elements are called letters.

We define the concatenation of any to letters $x,y\in\Sigma$ and denote this operation by the multiplication sign “$\cdot$”.

Using the concatenation, we can create words, also called strings $s$ over the alphabet $\Sigma$.

We denote by $\Sigma^*$ the set of all strings over the alphabet $\Sigma $.

Let $s\in\Sigma^*$ be a string. The length of the string, denoted by $|s|$, is defined as the number of concatenated letters which were used to create the string $s$.

Please note that $|s|\ge 0$ for any $s\in\Sigma^*$. If $|s|=0$, then we call $s$ the empty string and denote it by $\epsilon$.