User:Leigh.Samphier/Sandbox/Power Function on Base Greater than One is Unbounded Above

Theorem
Let $a \in \R$ be a real number such that $a > 1$.

Let $f: \Z_{\ge 0} \to \R$ be the real-valued function defined as:
 * $\map f n = a^n$

where $a^n$ denotes $a$ to the power of $n$.

Then $f$ is unbounded above.