You're right; sorry. I was stuck (as my comments indicate) on thinking of the classical setting of calculus, where functions can differ by a constant; but, since your functions are implicitly extended by 0, they cannot so differ! That is, unlike the constant function 0 : Z -> R, the 'constant' function 1 : N -> R isn't really constant once we regard it as a function Z -> R.

P.S. I am a mathematician; Python convinces me of nothing but special cases. :-)