I wanted to understand the Myhill-Nerode Theorem so I made up a small example to do so.
L = (a $+$ b )
Clearly, this language is regular. So, I should be able to establish a finite number of equivalence classes by using this method.
I start with a suffix of length 0, which is only $\lambda$:
a$\lambda$ = a $\in$ L
b$\lambda$ = b $\in$ L
For all suffix strings of length $\nu \gt 0$, both are not elements of L. Therefore, there are no distinguishable strings. I suspect this means there are 0 equivalence classes, and since 0 is a finite number, the language is regular. What might be missing from this analysis?
Note: I made sure to do some online research already and feel comfortable with the ideas of distinguishable strings. The equivalence class bit is what I probably need some clarification on.