Visual proof
Why You Cannot Divide by Zero
Not a rule mathematicians invented to spite you. A contradiction the universe refuses to sign off on. Here is the proof, the limit, the loophole, and why $\tfrac{0}{0}$ is worse than $\tfrac{1}{0}$.
Quick answer
Division by zero is undefined, not because mathematicians outlaw it, but because allowing it would force every number to equal every other number. The system can either keep arithmetic working or allow $\tfrac{1}{0}$. It cannot have both. $\tfrac{1}{0}$ is undefined because no number times zero equals one. $\tfrac{0}{0}$ is even worse, every number times zero equals zero, so "the answer" would be every number simultaneously. The first case has zero solutions; the second has infinitely many; either way, you cannot answer.
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