The title gives the property of density, which shows that there is a third real number between any two real numbers.

A is asking whether this axiom also applies to integers.

B is a strong proof of this axiom.

According to this answer, it should be possible.

A. No. Because the supply of real numbers is infinite. But limit that supply of integers.

B. If we always choose the middle point of any two real numbers. There is a 0.5 between 0 and 1, then 0.25 between 0 and 0.5, the next one is 0. 125, and then 0.0625. We can always find a new midpoint between 0 and the previous midpoint at infinity.

I hope the answer can help you.