I'm attempting to figure out if a union of two languages is regular.
$$ L_1 = \{all\ the\ words\ in\ the\ Oxford\ dictionary\} \\ L_2 = \{w : w\ has\ twice\ as\ many\ a's\ as\ b's\} $$
$L_2$ is well established to be a non-regular language. However, I am not sure if $L_1$ would be considered a regular language. The language should be finite (albeit large), which suggests it is regular, but I'm not certain.
If $L_1$ is regular, then I would consider the union $L_1 \cup L_2 $ would also be regular, as by the same argument, the language would be finite.
What does everyone think?