The set of all nonempty strings over an alphabet is denoted by  . That is,

Note that is infinite. It contains no infinite strings but strings of arbitrary lengths.

Reversal :
For any string the reversal of the string is .

An inductive definition of reversal can be given as follows:

Languages :
A language over an alphabet is a set of strings over  that alphabet. Therefore, a language L is any subset of . That is,  any is a language.