@NuclearStudent
It's difficult to say. What determines a person?
Memories? We forget stuff all the time. Not just little things, important things too. If you argue that amnesia makes you a different person, but forgetting minor things does not, then where do you draw that line? It has to be somewhere between forgetting what you had for breakfast and complete amnesia. But I've forgotten plenty of things, even foundation memories, and I'm still the same person.
Personality? Personality shifts over time are common, and a traumatic experience can lead to sudden shifts. Neither of these mark the death of a person though. Our desires and feelings may change. Are they what defines us? Even if we never had control over them to begin with? Even if you suddenly begin feeling and acting different, you still maintain a continuous stream of brain activity. Are we still the same person even if others see us as radically different?
The physical brain? If so, how much can be shaved away before we stop existing or become someone else? People have survived some incredible brain injuries in the past. Is it only total brain death that matters? What if you could split the brain in half and keep both halves alive? Would you then have two separate people? What if you put them back together? What would the subject experience? What would happen if you flash froze a brain, then thawed it out. Would it be like going to sleep and waking up, or would they have died and a new person been born in their place with all of their memories? How would you even know? Not every part of the brain is tied to higher thought. Which pieces could be replaced while maintaining the whole? What if you replaced the brain one cell at a time? Would there be a point where you become someone else, or would you still be yourself even when none of the original remained?
We start out as single cells with no awareness. Somewhere between there and adulthood we become conscious. Where is the dividing line? From before we are born to the moment we die, our brain activity never ceases. Even when we sleep or are knocked unconscious, it's still active, we just aren't aware of it. I would argue that so long as that brain activity is continuous, we exist as the same person. When it ceases for the last time, we die. But what if it's only temporarily interrupted. Do we persist? What if you slipped into a coma, and lived the rest of your life unconscious? Never aware, but still dreaming. If your conscious train of thought never returned would you still be yourself?
I guess what I'm saying is: it's complicated.