I remember encountering an instance when someone suggested that you could sum over a field other than the integers. I don't remember the exact topic, but I know someone here said it. How would one sum over a field, group, or ring? For that matter, how would you take an integral over a field, group, or ring (I don't mean field as in scalar or vector field, but rather in the sense of abstract algebra). I wasn't sure whether to put this in the abstract algebra or analysis thread, but decided on analysis.