The atman of Advaitaanta is the witness of the momentariness and its appearance and disappearances. What is momentary? Appearing and disappearing experiences. If there is no gap, then it will be a continuous experience. So continuous consciousness is proved even by the species of momentary consciousness. It has both existence and non-existence, appearance and disappearance. This is what is shining forth all else shines. Subject and object creator and created material world and subjective world. By its light, everything here is revealed, not only revealed, it is given existence.
Swami Sarvapriyananda teaches the Katha Upanishad, one of India's most revered texts which is also a part of the Vedas. It is a collection of philosophical poems representing a conversation between the sage Naciketas and Yama (god of death). They discuss the nature of Atman, Brahman and Moksha(liberation).