Question: is it possible to dream in a dream

Answer: Yes, A false awakening is a vivid and convincing dream about awakening from sleep, while the dreamer in reality continues to sleep. After a false awakening, subjects often dream they are performing daily morning rituals such as showering, cooking, cleaning, eating and using the toilet. False awakenings, mainly those in which one dreams that they have awoken from a sleep that featured dreams, take on aspects of a double dream or a dream within a dream. A classic example is the double false awakening of the protagonist in Gogol's Portrait (1835).