Word (Abstract Algebra)/Examples/Set with 2 Elements

Examples of Words in the Context of Abstract Algebra
Let $G$ be a group.

Let $X \subseteq G$ be a subset of $G$ such that $X = \set {a, b}$.

Then some of the elements of the set of words $\map W S$ of $G$ are:
 * $a, b, a b, b a, a b a, b a b, a^{-1} b, b a^{-1}, a b^{-1}, b^{-1} a, a b^{-1}, a^{-1} b^{-1}, a^{-1} b^{-1} a, \ldots$