We know that there are several different infinities, and there appears to be some kind of duality between infinity and zero. So how do we know that zero is unique? There as several distinct concepts of "nothing" in the english language that are often confused, as exemplified in the statement "nothing is better than eternal happiness, and a ham sandwich is better than nothing, so a ham sandwich is better than eternal happiness". The concept of nothing and its relation to zero and the empty set seems quite subtle. So to restate the question, how do we know that zero is unique?