Rule #1 of math: "You shall not divide by zero!"

So if you try to divide anything with zero, even zero itself, you violate the rule #1. If you do it anyway you can get any answer, i.e. you cannot ever trust the answer.

We have a function f(x) = x/x. What is f(0)?

f(0) = 0/0 = 1 because x/x is always = 1. Right?

We have another function f(x) = 0/x. What is f(0)?

f(0) = 0/0 = 0 because 0/x is always = 0. Right?

So now I have prooved that 0/0 is both =1 and =0. Right?

Wrong. I divided by zero in both cases, thus violated rule #1, and got a unreliable result. The proofs are worthless.

Conclusion: Do not ever try to divide by zero!