I would certainly call that another useful and valid perspective. Again, the real thing is to make sure you don't accidentally flipflop between them without re

I would certainly call that another useful and valid perspective. Again, the real thing is to make sure you don't accidentally flipflop between them without realizing it, because that leads to confusion. The mathematical definition isn't too hard, the definition I laid out isn't too hard, the definition you give isn't too hard, but the amount of confusion you can get from unknowingly switching between them is almost unbounded.