Well, you can divide 0 cakes between 2 people simply by giving them each 0 cakes. You have divided it up equally (i.e. both people have the same number of cakes), and if you take everything you gave them back, and combined them, you would get the 0 cakes you started with.
Dividing 2 cakes among 0 people truly is impossible. If you were giving away 2 cakes to 1 person, you would give away 2 cakes once. If you were giving away 2 cakes to 4 people, you would give away half a cake 4 times. How much cake do you have to give away 0 times, in order to give away both cakes? No amount will do. There will still be 2 cakes left.
More mathematically speaking, division of the number "b" by a number "a" is the unique solution for x in the equation:
a * x = b
So, for example, if we want to divide 4 by 2, we get 2. In terms of our equation, we need to solve for x:
2 * x = 4
We know that x has one and only one solution x = 2. Thus, we say that 4 / 2 = 2. What if we were to divide 2 by 0?
0 * x = 2
So, what is the one and only one solution of x? Well, this has no solution, since 0 * x = 0 for all x. Thus 2 / 0 is undefined. If we wanted to divide 0 by 0, then we are solving:
0 * x = 0
What is the one and only one solution of x? Well, any number x will satisfy this, so there's hardly only one solution! As an example, x = 0 and x = 1 are both solutions, so we have more than one solution, so 0 / 0 is also undefined.
