I agree that if we decide that 0 is the identity element then the concept of the kernel does have meaning. Well except that the article says the map isn't defined over {1111, 2222, 3333, ... , 9999} However 0 is just the additive identity and there's really no reason to select addition. We could just as easily select the multiplicative identity (1). So yes if you arbitrarily select 0 and then redefine function you can form a concept of the kernel (it's pretty boring as far as I can see).

However the article does specifically say that 6174 is the kernel. Now for that to be correct under your definition it would need to be true that: 7641 - 1467 = 0 Which we all know to be false. Your post seems to suggest that you think this use of kernel was a poor word choice instead of completely incorrect. Perhaps you could send me the details that your post promises.