Analysis I MT22, Scenic viewpoint theorem
Flashcards
In the proof of the scenic viewpoint theorem.
Let $(a _ n)$ be a sequence. Then $(a _ n)$ has a monotonic subsequence.
You consider a set
\[V = \\{k : \forall n>k,a_k \ge a_n\\}\]
What forms the monotonic subsequence in the case where $V$ is finite?
Let $(a _ n)$ be a sequence. Then $(a _ n)$ has a monotonic subsequence.
\[a_{N_1} < a_{N_2} < a_{N_3} < \ldots\]
where $N _ 1$ is the next point after the last peak, $N _ 2$ is the point larger than it, etc.