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.

Deeper iself-search  the fact that, the self is not the waking entity. If waking entity  is not the self then what is self  that witnesses these three states without the waking entity? 

The dream is witnessed as a whole without the physical apparatus.  Same way the waking experience also is witnessed  as whole 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. 

The self  is within the three states, as their formless substance. It is without 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 consciousness. 

Deeper self-search  is very much necessary to understand and assimilate the Self-knowledge or Brahma Gnana or Atma Gnana. 

Even though the self is something other than this waking entity (ego), the majority people still identify themselves with it.  The main reason people identify their-self with the waking entity (ego) is their ignorance of the Real Self.

Whosoever identifies his- self with this bundle of bones and flesh are caught up in the grip of duality. Now the question arises: If self is not this waking entity, then what is that self? The real self is not the waking entity but the formless soul, which witnesses the waking entity and waking world together.

The scriptures declare that self is the soul, the innermost self. The soul is present in the form of consciousness or Spirit —the three states are mere a mirage created out of the consciousness.  That's all.

The three states are is temporary, while the soul, the innermost Self is immortal Therefore, this  waking entity and waking experience is  false (impermanent), and the  Soul , the innermost Self is True (permanent).

The ultimate goal of human existence is to become re-established in reality of his true existence through Self-realization.  Self-knowledge of Brahma Gnana or Atma Gnana makes one realize the form, time and space are one in essence. That essence is the soul or consciousness.  Realizing the essence, which the soul or consciousness leads one to nondual self- Awareness.  In self-awareness there is only oneness in the midst of duality.