Dividing by Zero
Diving by zero is perhaps the most puzzling concept in math. How can you divide five cookies among zero people? When dividing 0 by 0, how many zeros are in zero? But why is dividing by zero undefined?
Firstly, lets try to divide by smaller and smaller positive numbers, trying to get as close to zero as possible.
As we divide one by smaller numbers, the quotient increases. One might say that dividing by zero is positive infinity. But what about negatives?
Same result. You could make an equally strong case that dividing by zero is negative infinity.
In Conclusion:
There is simply no good answer to dividing by zero. The current understanding of mathematical principals start to break when trying to explain dividing by zero. For now, mathematicians have decided to leave it undefined, as any other answer would be inconsistent with the rest of mathematics today.