Hi forum.
I'm trying to prove a claim from Mathematical Analysis I - Zorich since some days, but I succeeded only in part.
The complete claim is:
$$\left\{\begin{matrix} f\in\mathcal{C}^{(n)}(-1,1) \\ \sup_{x\in (-1,1)}|f(x)|\leq 1 \\ |f'(0)|>\alpha _n \end{matrix}\right. \Rightarrow \exists...
Homework Statement
I am trying to show that the integrator is unstable by giving examples of bounded inputs which produce unbounded outputs (i.e. a bounded function whose integral is unbounded).
Note: The integrator is a system which gives an output equal to the anti-derivative of its input...
Homework Statement
Prove if an ordered set A has the least upper bound property, then it has the greatest lower bound property.
Homework Equations
Definition of the least upper bound property and greatest lower bound property, set theory.
The Attempt at a Solution
Ok, I think that my main...