This is exactly why you have things like 0! = 1, 0 choose 0 = 1, 0^0 = 1, the empty sum is 0 and the empty product is 1, and so on. These are DEFINITIONS and th

This is exactly why you have things like 0! = 1, 0 choose 0 = 1, 0^0 = 1, the empty sum is 0 and the empty product is 1, and so on. These are DEFINITIONS and they make notation easier. They basically help the flow of mathematics. It's often difficult to watch someone try to explain "intuitively" why some of these things are the way they are and completely miss the point that they are like this because they help make other things easier.