The Division Algorithm says that $\displaystyle m=nq+r$, where $\displaystyle 0\leq r < n, n \geq 2$.

I understand that when $\displaystyle r=0$, $\displaystyle m $ is a multiple of n, or $\displaystyle m$ is divisible by n.

Technically, we say when $\displaystyle m=0$ and $\displaystyle r=0, n|0$.

Now, my question is this: When we divide $\displaystyle 0$ by $\displaystyle n$, we really have nothing to divide, but why $\displaystyle n|o$? Could anyone explain?