Deeper inquiry reveals the fact that, the self is not the waking entity(ego or you). If the waking entity is not the self, then what is it that witnesses these three states without the waking entity (you) ?
The dream is witnessed as a whole without the physical apparatus. Same way the waking experience also is witnessed by the same witness, which witnessed the dream as a whole.
The dream body and the dream world were within the dream. Same way the waking body and the waking world are within the waking experience. The formless witness, which is aware of the three states, is within the three states, but it is without the three states.
It is within the three states, as their formless substance. It is without the three states as their formless witness. The witness is apart from the three states, because it is formless, therefore it is not an entity or identity within the waking and dream.
The formless witness has to be grasped mentally to realize the fact that, the formless witness alone is real and eternal, and all the three states, which come and go, are mere mirage created out of the formless witness, which is in the form of the consciousness.
Deeper analysis is very much necessary to understand and assimilate the Self-knowledge or Bramha Gnana or Atma Gnana.