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

The set contains all the strings that can be generated by iteratively concatenating symbols from  any number of times.

Example : If = { a, b }, then =  { e, a, b, aa, ab, ba, bb, aaa, aab, aba, abb, baa, …}.

Please note that if , then   that is . It may look odd that one can proceed from the empty set to a non-empty set by iterated concatenation. But there is a reason for this and we accept this convention.