Read about bound | 3 Discussions | Page 1

  1. U

    I Boundedness of derivatives

    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...
  2. R

    Bounded functions with unbounded integrals

    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...
  3. S

    Proving least upper bound property implies greatest lower bound property

    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...