Correct me if I'm wrong but Arthas didn't die before we killed him right? And I really am requesting correction from someone who has either read Rise of the Lich King, or knows from another source on this matter.
I've been wondering lately, last time I was at the Frozen Throne, about Arthas being classed as Undead. When did he die? As far as I remember, he never died during WC3. After the Frostmourne mission, you just picked up as a grey skinned Death knight in the undead campaign working for Tichondrius to recover some acolytes in some city (what was that city by the way?). If he never died there, and not in WoW until we killed him ourselves, how could he be considered undead, since he never died? Do you somehow die upon becoming a death knight? Just what the hell is going on there? Perhaps Ner'zhul's posession of his body caused it?
Just what state of life or death is/was Arthas actually in before we put an end to his life?
Edit: I suppose Frostmourne could be responsible, but I don't remember witnessing Arthas dying because of a direct influence of the weapon, as I never saw Arthas go through the process of death period.