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Well, that is indeed possible and far more common then you might think.
To find out if you are being adversely affected by your poor sleeping habits, have a look at these common symptoms of sleep deprivation. Typical Signs of Sleep Deprivation and Insomnia… Irritability.
This is a growing anger and near hatred of everything and everyone around you. This symptom of sleep deprivation will cause you to snap at the littlest things and boil over in anger at the most trivial of mistakes. Tiredness.
In fact, doing nothing and thinking nothing sounds like the PERFECT idea and you want to start right now — even if you’re at work in the middle of a board meeting. Any task, be it big or small, is just too much work for you to handle and you want nothing more than to just sit or lay somewhere peacefully. You are quite literally sapped of energy.
Socially Inept. The things you say to people are incomprehensible and things said to you might as well be in a whole different language. Unlike the irritability symptoms of sleep deprivation, you’re fine with everyone around you and you don’t even mind talking to people — you just can’t understand what they are saying nor can you communicate effectively with them.
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Source: (symptoms of sleep deprivation) http://www.sleeptracks.org/symptoms-of-sleep-deprivation.html