Editing Kleene star (section)

== Definition ==
Given a set <math>V</math>,
define
:<math>V^{0}=\{\varepsilon\}</math> (the set consists only of the empty string),
:<math>V^{1}=V,</math>
and define recursively the set
:<math>V^{i+1}=\{wv: w\in V^{i} \text{ and } v\in V \}</math> for each <math>i>0.</math>
<math>V^i</math> is called the <math>i</math>-th power of <math>V</math>, it is a shorthand for the [[Concatenation#Concatenation of sets of strings|concatenation]] of <math>V</math> by itself <math>i</math> times. That is, ''<math>V^i</math>'' can be understood to be the set of all strings that can be represented as the concatenation of <math>i</math> members from <math>V</math>.

The definition of Kleene star on <math>V</math> is<ref>{{cite book |last1=Fletcher |first1=Peter |last2=Hoyle |first2=Hughes |last3=Patty |first3=C. Wayne |date=1991 |title=Foundations of Discrete Mathematics  |publisher=Brooks/Cole |isbn=0534923739 |page=656 |quote=The '''Kleene closure''' ''L''<sup>*</sup> of ''L'' is defined to be <math display="inline">\bigcup_{i=0}^\infty L^i</math>.}}</ref>

:<math> V^*=\bigcup_{i \ge 0 }V^i = V^0 \cup V^1 \cup V^2 \cup V^3 \cup V^4 \cup \cdots.</math>