User:Jshflynn/Definition:Word equality

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.