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OK well lets take a look at the rules of mathematics:
1. 0 over anything is 0.
2. Anything divided by 0 is inconclusive (meaning it does not exist).
These two rules conflict with one another, creating a paradox. So...the answer in my opinion is that 0/0 is non-existant. If you use a normal calculator to calculate, the answer is error :o
Your # 2 above wrong lah, for example 1 divided by zero is infinity meaning it does exist.