Bounded Below Real-Valued Function/Examples/Tangent on 0 to pi by 2

Example of Bounded Below Real-Valued Function
The real tangent function on the half-open interval $\hointr 0 {\dfrac \pi 2}$:


 * $\forall x \in \hointr 0 {\dfrac \pi 2}: \tan x$

is bounded below by $0$, but unbounded above.