Proving $\lim _{x \to 0^-} \frac{1}{x}=-\infty$ How do I calculate the limit:
$$\lim _{x \to 0^-} \frac{1}{x}$$
The answer is clearly $-\infty$, but how do I prove it? Its clear that as x approaches 0 from the right side, $x$, becomes infinitely small, but negative, making the limit go to $-\infty$, but how do I prove this mathematically?

If we say 
$$
\lim_{y \to x} f(y) = f(x)
$$ 
Then, for 'x' approaching 0 from negative side,
$$
\lim_{x \to 0^-} \frac{1}{x} = \lim_{-\frac{1}{n} \to 0^-} \frac{1}{\frac{1}{n}}= -\lim_{-\frac{1}{n} \to 0^-}n = -\infty
$$
