Definition:Word (Abstract Algebra)

Context: Group Theory
Let $$S \subseteq G$$ where $$G$$ is a group.

A word in $$S$$ is the group product of a finite number of elements of $$S$$.

The set of words in $$S$$ is denoted $$W \left({S}\right)$$:

$$\mathbf {Define:} \ W \left({S}\right) \ \stackrel {\mathbf {def}} {=\!=} \ \left\{{s_1 s_2 \ldots s_n: n \in \mathbb{N}^*: s_i \in S, 1 \le i \le n}\right\}$$

Note that there is nothing in this definition preventing any of the elements of $$S$$ being repeated, neither is anything said about the order of these elements.