I think not, because in the y=0 case the only sensible r is x, because remove the mod 0 subset you have the unmodified set of integers itself-- the remainder can only sensibly be an identity in that case.
> remove the mod 0 subset you have the unmodified set of integers itself-- the remainder can only sensibly be an identity in that case.
What are you talking about? There are no possible remainders mod 0 (just as there is one possible remainder mod 1 and there are 2 possible remainders mod 2) and there is no sensible definition of the remainder function; defining it to be identity is no less silly than defining it to be, IDK, 7.
No, x is an utterly non-sensible value of r.
> remove the mod 0 subset you have the unmodified set of integers itself-- the remainder can only sensibly be an identity in that case.
What are you talking about? There are no possible remainders mod 0 (just as there is one possible remainder mod 1 and there are 2 possible remainders mod 2) and there is no sensible definition of the remainder function; defining it to be identity is no less silly than defining it to be, IDK, 7.