Slow-wave sleep and dreaming sleep are vital partners in sleep. Dreaming sleep is thought to be of importance for learning, reasoning, controlling emotions, and other mental activity. Slow wave sleep is important because that's when proteins are built and when the brain and nervous system regain control over other body systems. (1)
Also see: What happens if you don't get sleep?
(1) Hartman, Ernest. "Sleep," The Worldbook Encyclopedia (Vol. 17). Chicago: World Book, 1990, pp. 507-508.
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