Today in math class, we were learning about asymptotes.

In our math book, it has written the following limits for a vertical asymptote:

$\displaystyle \lim_{x\rightarrow 0^+} \frac{1}{x}=+\infty$

and

$\displaystyle \lim_{x\rightarrow 0^-} \frac{1}{x}=-\infty$

He said that these two limits are wrong, because something can't equal infinity.

Is he right? Everywhere I have looked, these limits have been shown where it equals infinity, yet he says that these statements are false, and our mathbook is wrong for writing this.