On: Why you can't divide by zero

[4death4]

> The problem comes in when you repeat the exercise on a different example and find that also 0/0 = 3, or whatever. And now you start to see something is really amiss.

Yes, that's the obvious part.

[aeonik → 4death4]

That really sounds like it would be the identity.

If dividing by nothing is congruent with no operation, then the original set, unmodified should be returned.

[argiopetech → 4death4]

In this case, but the induction step is still important...