I got a basic idea on the item but still don't understand how do we know that our derivative is bounded by 1! If I understood well the magnitude of the derivative is bounded by epsilon which is 1 in our case?
Thanks again for all your help and time, you are so helpful. But since I can't use things that I have never been taught about in lectures I think I should use just the counterexample using an approximation. I really appreciate the time you spent for answering my questions!
Btw I gave a proof for the inequality you asked me in the other post, can you see it to tell me if you find it good?
Thank you very much!!!