Recent content by approx1mate

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    Is that subset of the set of continuous differential functions closed?

    Yes you are right again, thanks!
  2. A

    Is that subset of the set of continuous differential functions closed?

    I think that the solution is: |\left\langle f^n-f,cosh \right\rangle| \le \|f^n-f\|\|cosh\| But \forall \epsilon \ \ \exists n_o(\epsilon) such that for any n \ge n_0(\epsilon) we have that: |\left\langle f^n-f,cosh \right\rangle| \le \epsilon \|cosh\| Therefore \left\langle...
  3. A

    Is that subset of the set of continuous differential functions closed?

    Oh yes, I am sorry, all that time I didn't pay any attention to the definition of W. Thanks
  4. A

    Is that subset of the set of continuous differential functions closed?

    You are right, I was wrong about that. Ok, that was my thought from the very beginning. But if I need just the f(1)=0, then how do I know that the limit f is also a continuous differentiable function? Don't I need that as well?
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    Is that subset of the set of continuous differential functions closed?

    Hi! I have used the physics forum a lot of times to deal with several tasks that I had and now its the time to introduce my own query! So please bear with me :-) Homework Statement Equip the set C^1_{[0,1]} with the inner product: \left\langle f,g \right\rangle= \int_{0}^{1}...