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 or characters and call it $V$, and create a never-ending infinite list from all the numbers/characters of that set, with all the combinations that are possible by reusing any of those numbers/characters, even multiple times, 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, including number or character reusage.

Characters can be reused unlimited times, which is why the list is infinite.

Example

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", ...}.