Just a random question that popped in my head. This is of course non true if we consider just irrationals.
Moreover, (assuming above holds) does there exists some sort of equivalence class for transcendentals such that $x\sim y$ iff $\exists f,g$ non zero algebraic st $f(x)=g(y)$.
If it does, then for each given transcendental, is it dense on $\mathbb R$?
Please feel free to add tags as I'm not sure about category for this question
It is not known if $e+\pi$ is algebraic or not.