It's undefined. What did you expect? A miracle, perhaps?

There's a reason your first year Calculus prof made your life miserable with epsilons and deltas (and if she didn't, there's a reason she should have done). Some things are numbers: 0, 17, 0.1234567891011121314..., pi. But not everything is a number; some things just aren't: a banana, a dodecahedron, "1 divided by zero". When we call something a number, we expect to be able to perform various operations on it. Deep, complex, mathematical operations like addition and multiplication. (Maybe even a few more complicated ones, but these 2 will do.)

So who cares about some snotty mathematician's prejudices that "that's not what I call a number!"? Well, you should! Say 1/0 is a number; call it x. Well, 2/0 should be 2x (= x+x). Now we have that 1/x = 1/(1/0) = 0, which is cool, until you realise that then 1/(2x) = 0/2 = 0 = 1/x, so 2x=x and therefore 1/0=x=0, which is clearly wrong.

Conclusion: It's not possible meaningfully to define 1/0 to be a number. Sorry.