asymptote of an arctangent

Given the function $y={\tan }^{-1}(x)$,

we see that it has two asymptotes, namely $\frac{\pi }{2}$ and $-(\frac{\pi }{2})$. This specific example of an asymptote was mentioned in an episode of the comedy TV show The Big Bang Theory, in which the mathematician Sheldon Eppes tries to explain his inability to reach the top of a rock wall, getting stuck at the same height each time. According to the Mathematica manual, the results of ArcTan for real $z$ ”are always in the range $-\pi /2$ to $\pi /2$.