Definition
Let $\Sigma$ be an alphabet and let $x$ and $y$ be words over $\Sigma$.
Then $x$ and $y$ are defined to be equal iff:
- $\operatorname{len}(x) = \operatorname{len}(y)$ and $\forall i: x_i = y_i$
That is, iff their lengths are equal and each of their respective letters are equal.