How was "Denzel Washington" able to show up at the end in the movie "Deja-Vu"?

Question

Near the end of the movie, he had died in the explosion. . & then he came walking up to the woman he had fallen in love with that he'd seen through the time-device- but completely unaware of what had just happened to himself earlier. In other words, if he left that one time-line & then died, how could he then come walking up to the woman still alive? I know this question regarding time-travel is confusing- that is why I am asking though. Would appreciate thoughts, ideas, theories, science from all. Thank you!!

Answer 1

i think that when he stopped the ferry from blowing up that he completely altered the time line, even the past. cause i remember the scientists saying that they would exist, but not that "version" of them.  

Answer 2

He was still alive in the past, therefore when future Denzel died, his present self was still alive.

Answer 3

Remember, he went back in time to before the attack on the boat and saved all the lives of the people on the boat.  So because there was no terrorist attack on the boat, he never had to meet Val Kilmer's character who then showed him the time viewing machine.  He just went on not really knowing what happened except for the girl who met the future version of himself.