Empty Group Word is Reduced

Theorem
Let $S$ be a set

Let $\epsilon$ be the empty group word on $S$.

Then $\epsilon$ is reduced.

Proof
By definition, a group word $w$ is reduced $w_i \neq w_{i+1}^{-1}$ for all $i \in \{1, \ldots, n-1\}$, which is vacuously true for $\epsilon$.