alphabet

an alphabet is a finite, non-empty set of symbols. conventionally, we use the symbol for an alphabet. common alphabets include:

1. , the binary alphabet.
2. , the set of all lower-case letters.
3. the set of all ASCII characters, or the set of all printable ASCII characters.

if is an alphabet, we can express the set of all strings of a certain a certain length from that alphabet by using an exponential notation. we define to be the set of strings of length , each of whose symbols is in .

the set of all strings over an alphabet is conventionally denoted . for instance, . put another way, sometimes we wish to exclude the empty string from te set of strings. the set of nonempty strings from alphabet is denoted . thus, two appropriate equivalences are:

• .
• .