An additional problem is that due to the existence of this tag, a user entering "differential geometry" in the tag field automatically gets the question tagged with (differential) and (geometry), not with (differential-geometry). — Normal Human 3 hours ago
Prove that $\{2^n : n \in \mathbb{N} \}$ is not bounded.
Proof: By Induction; $2^n \geq n,\forall n \geq 1$.
By Archimedean property $\mathbb{N}$ is not bounded above.
Assume that $\{2^n : n \in \mathbb{N} \}$ is bounded.
Then $\exists M \in \mathbb{R}\gt 0$
such that $\forall n, n \leq 2^n...
