Proving a Language is Irregular using Myhill-Nerode I'm trying to prove that the language: \begin{equation*}
L = \{ w \in \{ 0, 1 \}^* : w  \text{ contains more 0's than 1's} \}
\end{equation*} is irregular using the Myhill-Nerode theorem. I've been through all the basic examples in the book, and thought I understood them, but I'm having trouble with this one.

So far, I've been thinking about letting $ x_i = 1^i 0^i $ and $x_j = 1^{j+1} 0^{j-1}$, then if I let $ w_{ij} = 0$, only $x_iw_{ij} \in L$. That seems to be sufficient, but it seems weak compared to some of the other examples.

Am I on the right track here? I would really appreciate any hints/suggestions.
You need to come up with an infinite number of pairwise inequivalent strings. Try $x_i = 0^i$ for all $i \geq 0$.