Empty set is closed under addition. If not, there would be at least one element in the empty set whose addition with itself is not there, contradiction. Thus the result follows. This not a convention, but a claim, right?
Empty sum is defined to be zero. This is a convention.
But these two contradict each other. Empty set should contain zero then. What am I missing? Can a convention contradict a claim?
(By the way, this is not my own question, I heard it over from some student in BU, Turkey)