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 \(\epsilon\).
| | | | | created: 2014-06-22 15:42:14 | modified: 2020-05-09 21:01:11 | by: bookofproofs | references: 
 Knauer Ulrich: “Diskrete Strukturen – kurz gefasst”, Spektrum Akademischer Verlag, 2001