Powers of Strings : For any string x and integer 
, we use 
to denote the string formed by sequentially concatenating n copies of x. We can also give an inductive definition of as follows:
= e, if n = 0 ; otherwise 
, we use to denote the string formed by sequentially concatenating n copies of x. We can also give an inductive definition of as follows: = e, if n = 0 ; otherwise 
= 011011011, 
= 011 and 
Powers of Alphabets :
We write 
(for some integer k) to denote the set of strings of length k with symbols from 
. In other words,
= { w | w is a string over and | w | = k}.
Hence, for any alphabet, 
denotes the set of all strings of length zero. That is, = { e }. For the binary alphabet { 0, 1 } we have the following.
