TITLE: Dividing a number by zero
QUESTION [5 upvotes]: Why can't you divide a number by zero?
It is possible to say $\sqrt{-1}$ is an imaginary number $i$, but why can't you say $\frac{1}{0}$ is also an imaginary number $z$ (for example)?

REPLY [5 votes]: Another way to see the problem is by looking at limits:
$$\displaystyle \lim_{x->0^+} \frac{1}{x} = \infty$$
But:
$$\displaystyle \lim_{x->0^-} \frac{1}{x} = -\infty$$
And since there's no preference to any one-sided limit, the limit should not exist and there isn't a specific value to the function $\frac1x$ at 0.