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