What is nothing divided by Nothing? Zero divided by Zero. Much has been written about this topic. Here are a few of my favorites:

• A. Khan Academy
• B. Physics Forum
• C. Know Your Meme

From the comments on (A) this is my favorite explanation: "It's like saying all the cars I own are Ferraris, which is true because I don't own any cars. I have no cars and no Ferraris."

Undefined versus Indeterminate

Given that, you can see the difference between 1/0 and 0/0. We say that 1/0 is undefined because there is no number c that satisfies 0xc = 1. On the other hand, any number c satisfies 0xc = 0 and there's no reason to choose one over any of the others, so we say that 0/0 is indeterminate.

Indeterminate is not the same as undefined. It essentially means that if it pops up somewhere, you don't know what its value will be in your case! That's the premise behind the meme in reference C!

The definition of division states: a/b = c if and only if c x b = a. In other words, if you cannot reverse a division by multiplication it does not fit the definition.