multiplication is a more complex addition...division, i'm told by the internet, is a more complex form of subtraction. we subtract the divisor from the dividend and continue until we reach a point that no whole divisors appear, and that is our remainder.
personally, I kinda find this moronic. at divide by 0, you subtract zero from the dividend, and get an answer...a unity...the same number split into 0 pieces. The undefined in the computer (so says teh intertubes) is that this complicated subtraction is continued ad infinitum until exception and halting...for undefined.
i also believe that the type of zero you are talking about is VERY important, as like infinity, zero is not a number but a concept...and given humanity's provincial "never being wrong" attitude...i ask this...could there be more than one type of zero? In Newtonian gravity, divide by zero when the distance between two objects becomes zero results in "undefined". Personally, i look at this event in my head and realize that if the two objects are 0 distance apart, you could easily (depending on composition and actual mass) you would no longer have two objects...no distance between centers of mass, since you only now have one mass. This zero specifically refers to the distance between two bodies of mass moving towards each other...wouldn't the equation change once there is only one body, no distance to travel...just a unified single object possibly in motion?
so this is going to get a little into sort, quicksort, and heapsort arguement. what kind of divisions would result in actual numbers, should we simply change how we divide? how about removing single units into a number of piles equal to the divisor and the remainder is still the same? In this scenario though, it would seem to give a real answer though, instead of getting stuck in a loop because we programmed everything to 'kernel panic' and can't decide when to stop subtracting nothing...dividing into no piles...no division when 0 in the denominator.
So if it's a 0 of a distance, would indicate no distance...if it's a zero of a charge, would indicate no charge...if it's a zero of mass, it would indicate no mass...