Unsolvable problem

BORED!!! So bored that I have to write this lame pose!(Actually I have 3 tests to prepare for and 3 assignments to rush but I'm lazy :P) Back to the topic, what is this unsolvable problem which I speak of? Well, it is none other than the simple yet undeniably neurone-disintegrating question, what is 0/0?

Yes, of course we know that anything divided by zero is undefined, simply because how could you divide with nothing? However, we also learned that a number, when divided with itself, gives us an answer of 1. Example, 5/5 = 1 and 1092.3/1092.3 = 1. So does this also mean 0/0 = 1? And of course, we also learned that zero divided by anything, remains zero. So what is the real answer? Well, professors are arguing over this matter and we shall leave it up to them in solving this impossible question.

So what do you guys think? Is the answer undefined, zero, or even one?