Divergent Real Sequence to Positive Infinity/Examples/2^n/Proof 1

Proof
Let $H \in \R_{>0}$ be given.

By Boundedness of Nth Powers, $\sequence {a_n}$ is unbounded above.

Hence:
 * $\exists N \in \N: 2^N > H$

Then if $n > N$, we have:


 * $2^n > 2^N > H$

and the result follows.