Originally posted by goddess_susu
"By attempting to kill you, Voldemort himself singled out the remarkable person who sits here in front of me, and gave him the tools for the job! It is Voldemort's fault that you were able to see into his thoughts, his ambitions, that you even understand the snakelike language in which he gives orders, and yet, Harry, despite your privileged insight into Voldemort's world — which, incidentally, is a gift any Death Eater would kill to have — you have never been seduced by the Dark Arts, never, even for a second, shown the slightest desire to become one of Voldemort's followers!"
"Of course I haven't! He killed my mum and dad!"
"You are protected, in short, by your ability to love. The only protection that can possibly work against the lure of power like Voldemort's."
-Dumbledore and Harry [HPHBP, ch.24]PART 2: "and either must die at the hand of the other for neither can live while the other survives"
DEFINITONS OF EITHER:
#1- Any one of two; one or the other
#2- *THE ONE AND THE OTHER OF TWO*
DEFINITION OF NEITHER:
#1- Not one or the other; not eitherSo, rephrasing
"Both Harry and Voldemort will die at the hand of the other, because not one or the other can live while the other is alive."Prediction: Since they complete each other, Harry and Voldemort will reunite (maybe like they did in OOTP). Harry, being able to love beyond all costs and not being afraid of death, will take his own life, and Voldemorts.
I'm sorry but that is not what the prophecy means. The definitions that you provided are both referring to it being one or the other so the prophecy indicates that only one of them has to die whether if its Harry or Voldemort. They both can't die at the same time because that would just be adding insult to the injuries that Harry has suffered throughout this series so he must survive.