Breathing is difiened as the active intake of gases for the purpose of respiration, and the passive release of waste gases.
Alive in the case of humans falls under your ability to comprehend your surroundings and be self awareness.
Plus all the other simple factors, that i cant remember from biology at the moment. The whole thing of brain dead falls under the whole keeping people on life support thing, is it wrong to keep people in the world just because they where someone to us once, or should we let them go? You decide?
Lol, sounds like a reality tv show, maybe we'll have that for when bush dies, it'll be the largest tele-vote ever recorded from iraq and veterans alike.
Sorry, off topic.