Question

describe the set C f: I ---> R
for which
\[\forall x,y \in I

\left| f(x)-f(y)\right| \le \sin ^{2} (x-y) \]


please help !

Answer 1

\(\large C:= \lbrace f: I \to \mathbb{R}, \ \forall x,y \in I \mid |f(x)-f(y)| \leq \sin^2(x-y) \rbrace \) ?

Answer 2

yes it is.. do you have an idea ?

Answer 3

I am not sure what they want you to do when they say describe the set, check if the set is bound/unbound, open/closed, empty/nonempty?

Answer 4

any idea ?