+118608 $$\.. \hspace{80pt} \ \lim\limits_{x \to +0}{\frac{c}{x}} = \infty\ where\ c = positive\: const \\\\
\.. \hspace{80pt} \ \lim\limits_{x \to -0}{\frac{c}{x}} = -\infty\ where\ c = positive\: const$$
This is why it is undefined. If you approach zero from above it is +infinity. If you approach from below it is negative infinity.
Here is a graph (in this one c=1 but it could be any pos constant.)
+128448 Undefined...to see why.....consider
6/2 = 3 because 3 x 2 = 6
But what is 3/0 ??
3/0 = ??? ..... In other words.....what multiplied by 0 returns 3 ???
Answer.......nothing !!! Whatever "it" is.......we can't define it!!!
Also. we have an "indeterminate" form which is 0/0......What is 0/0 ??
I claim it could be anything........ it could be 11 or it could be "pi".....(can you see why???)
+576 Well it sort of depends. I once asked a professor this question and he responded with, "it blows up, like a bomb."
One way I like to think of it is in a real context. First of all lets say I had no hamburgers and five friends, and I wanted to share my hamburgers with my friends. since there are six of us this is 0/6. The question, then, is how much food do each of my friends get? None of course because there is no food! Now we flip the script. Lets say i have six burgers but i have not friends to share them with. How many burgers do each of my friends get? Mathematically this looks like 6/0 and at first many people think this is also zero. Consider it more closely though, the question was how many burgers do each of my friends get? Since I have no friends in this context it the question makes no sense and therefore we cannot answer the questions. When we run into things like this in math we say they are undefined.
another answer to this is infinity. Pick a number, any number and divide it by 1. Then divide by .5, then by .2 then .1. Divide it by .01 and .001 and .0001 and notice the pattern. The numbers get massive! This is undoubtedly what my professor meant when he said it blows up like a bomb!
Your professor’s comment notwithstanding, in the set of real numbers, the solution is never infinity. There may be infinite solutions, and any one of them shares validity with all the others, this is why it is undefined. However, infinity is not a solution to division by zero. This also applies to zero divided by zero.
The above is a basic rewording of what CPhill described (He knows a lot about zero’s --especially Roman zeros).
The professor’s “b**w-up” comment may be a metaphor referring to the concept basis that is depicted in the equation below.
$$\.. \hspace{75pt} \ \lim\limits_{x \to 0}{\frac{c}{x}} = \infty\ where\ c = const$$
Here X is an asymptote. It never actually reaches zero.
+118608 $$\.. \hspace{80pt} \ \lim\limits_{x \to +0}{\frac{c}{x}} = \infty\ where\ c = positive\: const \\\\
\.. \hspace{80pt} \ \lim\limits_{x \to -0}{\frac{c}{x}} = -\infty\ where\ c = positive\: const$$
This is why it is undefined. If you approach zero from above it is +infinity. If you approach from below it is negative infinity.
Here is a graph (in this one c=1 but it could be any pos constant.)
+118608 It is interesting.
We all agree that when you divide by zero the answer is undefined. But we all have different reasoning.
Some of our reasons appear to be contradictory. 
I have done it via limits but anonymous appears to be correct when s/he says that it is not a limit question.
It has just got me thinking a little. That is all.
+118608 A newer related post.
http://web2.0calc.com/questions/why-some-simple-calculations-are-impossible
