That opens up all kinds of cans of worms. Let's say you are put into a medical coma, no thoughts, only eniugh activity to sustain life. You're scanned, and a perfect copy of you is made. You both wake up in another room, at exactly the same time. Are both versions of you equally "you?" You don't know which is which. Does the answer change if a 3rd party knows, or there is no knowledge of which is which? If all that matters is continuous stream of consciousness, then I suppose the answer would be you died in the coma, and two people with your memories were born, I suppose.