As this diagram shows, energy levels get closer together as they get higher. Is a free electron then truly free? Or is it in such a high (bound) state of energy that the transitions become nearly (but not actually) continuous?
If the latter is true, then wouldn't every electron in the universe in fact be bound to every nucleus, just mostly at very high energy levels? Or is this understanding wrong, and instead there is a clear cut distinction between the bound and unbound electron? In that case, what defines the transition?