TITLE: Why Limit of $0/x$ is $0$, if $x$ approaches $0$?
QUESTION [12 upvotes]: It might be a silly question, but to me it is not obvious why the following expression holds:
$$
\lim\limits_{x\rightarrow 0}\frac{0}{x}=0 ?
$$

REPLY [16 votes]: $$\frac0{1}=0$$
$$\frac0{0.1}=0$$
$$\frac0{0.01}=0$$
$$\frac0{0.001}=0$$
$$\frac0{0.0001}=0$$
$$\frac0{0.00001}=0$$
$$\frac0{0.000001}=0$$
$$...$$