Logic puzzle, numbers on the back of head

Question

Ok, I found this puzzle and I can't figure out the answer:

Two people, Albert and Bernard have a natural number {0,1,2,3 ...} on the back of their heads. Rules:

1. They can't see their own number
2. Albert stands in the back of Bernard, so he can see Bernards number
3. One of the numbers is the immediate successor of the other (in any order), so: na = nb+1 or nb = na+1

Then, these questions are asked:

To Albert: Do you know whether your own number is equal to 0?
Alberts answer: I know that my number is NOT equal to 0.

To Bernard, same question.
Answer: ?
(I thought he couldn't know. Since Bernard can still be zero, while Albert is 1)

To Albert: Do you know whether your own number is equal to 1?
Albert' answer: I don't know

To Bernard, same question.
Answer: ?
(I still think he couldn't know)

After this, you are supposed to know what Bernards number is. But how?

Answer 1

That albert say:

I know that my number is NOT equal to 0.

Means that Bernards number does not equal to $1$, since in this case Alberts number could be 0. When Albert answer

I don't know

To the question wether he has the number 1, this gives us lot of information:

1. Bernard could not have $0$, since if he had $0$, Albert would know that he had $1$.
2. If Bernard had a number greater than or equal to $3$ then Albert would know that his number was not $1$.
3. If Bernard had the number $1$ then Bernard would know that he could not also have the number $1$.

Thus the only possible number which Bernard could have is $2$. Thus Bernad will say that he knows the second time he is asked, while the first time he is asked he says he do not know.