Power Function on Base Greater than One is Strictly Increasing/Positive Integer

Theorem
Let $a \in \R$.

Let $a > 1$.

Let $f: \N \to \R$ be the real-valued function defined as:
 * $f \left({ n }\right) = a^n$

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

Then $f$ is strictly increasing.

Proof
Fix $n \in \N$.

Hence the result.