Kleene star

In mathematical logic and computer science, the Kleene star (or Kleene operator or Kleene closure) is a mathematical process or operation on sets of numbers, characters (like letters) or symbols. It is often used for regular expressions.

As an example, if we take a set of numbers and call it $V$, and create a never-ending list of all the numbers in that set, in all the combinations that are possible with those numbers, then we have created the Kleene star of $V$. So, given a set, it's the set of all string combinations of members of that set.

Examples

Let's create a set called V, and put the symbols a and b in it.

V = {a, b}

So here's the Kleene star applied to that set of characters:

{"a", "b"}⁺ = { "a", "b", "aa", "ab", "ba", "bb", "aaa", "aab", ...}.