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 \(\epsilon\).
Applications: 1
Chapters: 2 3 4 5
Corollaries: 6
Definitions: 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
Examples: 28 29 30 31 32 33 34 35 36 37
Parts: 38
Proofs: 39 40 41 42
Propositions: 43