You're noticing the algebraic numbers + all the transcendentals that you happen to need throughout your life (\pi, e, etc.) are countable. Sounds kind of deep,

You're noticing the algebraic numbers + all the transcendentals that you happen to need throughout your life (\pi, e, etc.) are countable. Sounds kind of deep, but plenty of proofs apply to uncountable sets. We finite little humans just live, necessarily, in a countable world.